diff --git a/tools/workspace/default.bzl b/tools/workspace/default.bzl
index 5b6ca2c7b512..1605e7fb280b 100644
--- a/tools/workspace/default.bzl
+++ b/tools/workspace/default.bzl
@@ -36,6 +36,7 @@ load("@drake//tools/workspace/glx:repository.bzl", "glx_repository")
 load("@drake//tools/workspace/googlebenchmark:repository.bzl", "googlebenchmark_repository")  # noqa
 load("@drake//tools/workspace/gtest:repository.bzl", "gtest_repository")
 load("@drake//tools/workspace/gurobi:repository.bzl", "gurobi_repository")
+load("@drake//tools/workspace/gym_py:repository.bzl", "gym_py_repository")
 load("@drake//tools/workspace/gz_math_internal:repository.bzl", "gz_math_internal_repository")  # noqa
 load("@drake//tools/workspace/gz_utils_internal:repository.bzl", "gz_utils_internal_repository")  # noqa
 load("@drake//tools/workspace/ibex:repository.bzl", "ibex_repository")
@@ -84,6 +85,7 @@ load("@drake//tools/workspace/scs:repository.bzl", "scs_repository")
 load("@drake//tools/workspace/sdformat_internal:repository.bzl", "sdformat_internal_repository")  # noqa
 load("@drake//tools/workspace/snopt:repository.bzl", "snopt_repository")
 load("@drake//tools/workspace/spdlog:repository.bzl", "spdlog_repository")
+load("@drake//tools/workspace/stable_baselines3_internal:repository.bzl", "stable_baselines3_internal_repository")  # noqa
 load("@drake//tools/workspace/statsjs:repository.bzl", "statsjs_repository")
 load("@drake//tools/workspace/stduuid:repository.bzl", "stduuid_repository")
 load("@drake//tools/workspace/styleguide:repository.bzl", "styleguide_repository")  # noqa
@@ -191,6 +193,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
         gz_math_internal_repository(name = "gz_math_internal", mirrors = mirrors)  # noqa
     if "gz_utils_internal" not in excludes:
         gz_utils_internal_repository(name = "gz_utils_internal", mirrors = mirrors)  # noqa
+    if "gym_py" not in excludes:
+        gym_py_repository(name = "gym_py", mirrors = mirrors)
     if "ibex" not in excludes:
         # N.B. This repository is deprecated for removal on 2023-02-01.
         # For details see https://github.com/RobotLocomotion/drake/pull/18156.
@@ -289,6 +293,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
         snopt_repository(name = "snopt")
     if "spdlog" not in excludes:
         spdlog_repository(name = "spdlog", mirrors = mirrors)
+    if "stable_baselines3_internal" not in excludes:
+        stable_baselines3_internal_repository(name = "stable_baselines3_internal", mirrors = mirrors)  # noqa
     if "statsjs" not in excludes:
         statsjs_repository(name = "statsjs", mirrors = mirrors)
     if "stduuid" not in excludes:
diff --git a/tools/workspace/gym_py/BUILD.bazel b/tools/workspace/gym_py/BUILD.bazel
new file mode 100644
index 000000000000..2e5301dc6578
--- /dev/null
+++ b/tools/workspace/gym_py/BUILD.bazel
@@ -0,0 +1,8 @@
+# -*- python -*-
+
+# This file exists to make our directory into a Bazel package, so that our
+# neighboring *.bzl file can be loaded elsewhere.
+
+load("//tools/lint:lint.bzl", "add_lint_tests")
+
+add_lint_tests()
diff --git a/tools/workspace/gym_py/README.md b/tools/workspace/gym_py/README.md
new file mode 100644
index 000000000000..5e24c0bdcd59
--- /dev/null
+++ b/tools/workspace/gym_py/README.md
@@ -0,0 +1,4 @@
+gym
+===
+
+This imports the OpenAI Gym RL tool into our build.
diff --git a/tools/workspace/gym_py/package.BUILD.bazel b/tools/workspace/gym_py/package.BUILD.bazel
new file mode 100644
index 000000000000..0f08296fda46
--- /dev/null
+++ b/tools/workspace/gym_py/package.BUILD.bazel
@@ -0,0 +1,12 @@
+# -*- python -*-
+
+load("@drake//tools/skylark:py.bzl", "py_library")
+
+licenses(["notice"])  # MIT
+
+py_library(
+    name = "gym_py",
+    srcs = glob(["gym/**/*.py"]),
+    imports = ["gym"],
+    visibility = ["//visibility:public"],
+)
diff --git a/tools/workspace/gym_py/repository.bzl b/tools/workspace/gym_py/repository.bzl
new file mode 100644
index 000000000000..763167e121fc
--- /dev/null
+++ b/tools/workspace/gym_py/repository.bzl
@@ -0,0 +1,15 @@
+# -*- python -*-
+
+load("@drake//tools/workspace:github.bzl", "github_archive")
+
+def gym_py_repository(
+        name,
+        mirrors = None):
+    github_archive(
+        name = name,
+        repository = "openai/gym",
+        commit = "v0.21.0",
+        sha256 = "0efc4ca01fa0d0cd10391b37db0c52e09084fb7a3fd04cdc68e08081acbf4418",  # noqa
+        build_file = ":package.BUILD.bazel",
+        mirrors = mirrors,
+    )
diff --git a/tools/workspace/stable_baselines3_internal/BUILD.bazel b/tools/workspace/stable_baselines3_internal/BUILD.bazel
new file mode 100644
index 000000000000..f6a2c24960a6
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/BUILD.bazel
@@ -0,0 +1,14 @@
+# -*- python -*-
+
+# This file exists to make our directory into a Bazel package, so that our
+# neighboring *.bzl file can be loaded elsewhere.
+
+load("//tools/lint:lint.bzl", "add_lint_tests")
+load("//tools/skylark:drake_py.bzl", "drake_py_unittest")
+
+drake_py_unittest(
+    name = "stable_baselines3_internal_test",
+    deps = ["@stable_baselines3_internal//:stable_baselines3"],
+)
+
+add_lint_tests()
diff --git a/tools/workspace/stable_baselines3_internal/README.md b/tools/workspace/stable_baselines3_internal/README.md
new file mode 100644
index 000000000000..5a0cc5c4d0ff
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/README.md
@@ -0,0 +1,32 @@
+stable_baselines3_internal
+==========================
+
+A local import of `stable_baselines3` that *does not* have its dependencies
+(such as `pytorch`).  As such, code using this module will have a
+`ModuleNotFoundError` error if it attempts to use any functions that depend on 
+those modules.
+
+The resulting `stable_baselines3` workalike is available via the bazel::
+
+  deps = [
+      "@stable_baselines3_internal//:stable_baselines3",
+  ],
+
+and then, in python::
+
+  import stable_baselines3
+
+Code that wants to import the most featureful version of `stable_baselines3`
+available (i.e., to use a locally installed `stable_baselines3` if available
+and the Drake-provided workalike otherwise) can rely on the presence of the
+string `"drake_internal"` in the `__version__` attribute.  For instance::
+
+  sb3_is_fully_featured = False
+  try:
+      import stable_baselines3
+      if "drake_internal" not in stable_baselines3.__version__:
+          sb3_is_fully_featured = True
+      else:
+          print("stable_baselines3 found, but was drake internal")
+  except ImportError:
+      print("stable_baselines3 not found")
diff --git a/tools/workspace/stable_baselines3_internal/connection.patch b/tools/workspace/stable_baselines3_internal/connection.patch
new file mode 100644
index 000000000000..956e2270eeb1
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/connection.patch
@@ -0,0 +1,11 @@
+diff --git a/stable_baselines3/common/vec_env/subproc_vec_env.py b/stable_baselines3/common/vec_env/subproc_vec_env.py
+index f723c71..43fa394 100644
+--- stable_baselines3/common/vec_env/subproc_vec_env.py
++++ stable_baselines3/common/vec_env/subproc_vec_env.py
+@@ -1,5 +1,6 @@
+ import multiprocessing as mp
+ from collections import OrderedDict
++from multiprocessing import connection
+ from typing import Any, Callable, List, Optional, Sequence, Tuple, Type, Union
+ 
+ import gym
diff --git a/tools/workspace/stable_baselines3_internal/no_torch.patch b/tools/workspace/stable_baselines3_internal/no_torch.patch
new file mode 100644
index 000000000000..eae5b22bda90
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/no_torch.patch
@@ -0,0 +1,96 @@
+diff --git a/stable_baselines3/__init__.py b/stable_baselines3/__init__.py
+index d73f5f0..5797dba 100644
+--- stable_baselines3/__init__.py
++++ stable_baselines3/__init__.py
+@@ -1,13 +1,19 @@
+ import os
+ 
+-from stable_baselines3.a2c import A2C
+-from stable_baselines3.common.utils import get_system_info
+-from stable_baselines3.ddpg import DDPG
+-from stable_baselines3.dqn import DQN
+-from stable_baselines3.her.her_replay_buffer import HerReplayBuffer
+-from stable_baselines3.ppo import PPO
+-from stable_baselines3.sac import SAC
+-from stable_baselines3.td3 import TD3
++def not_loaded(name):
++    raise ImportError(f"{name} not in Drake's internal stable_baselines3")
++
++def make_not_loaded(name):
++    return lambda *args, **kwargs: not_loaded(name)
++
++A2C = make_not_loaded("A2C")
++get_system_info = make_not_loaded("get_system_info")
++DDPG = make_not_loaded("DDPG")
++DQN = make_not_loaded("DQN")
++HerReplayBuffer = make_not_loaded("HerReplayBuffer")
++PPO = make_not_loaded("PPO")
++SAC = make_not_loaded("SAC")
++TD3 = make_not_loaded("TD3")
+ 
+ # Read version from file
+ version_file = os.path.join(os.path.dirname(__file__), "version.txt")
+diff --git a/stable_baselines3/common/env_checker.py b/stable_baselines3/common/env_checker.py
+index 3b2c502..392d9df 100644
+--- stable_baselines3/common/env_checker.py
++++ stable_baselines3/common/env_checker.py
+@@ -6,7 +6,13 @@ import numpy as np
+ from gym import spaces
+ 
+ from stable_baselines3.common.preprocessing import is_image_space_channels_first
+-from stable_baselines3.common.vec_env import DummyVecEnv, VecCheckNan
++
++torch_available = False
++try:
++    from stable_baselines3.common.vec_env import DummyVecEnv, VecCheckNan
++    torch_available = True
++except ImportError:
++    print("Torch not available; skipping vector env tests.")
+ 
+ 
+ def _is_numpy_array_space(space: spaces.Space) -> bool:
+@@ -87,6 +93,8 @@ def _check_unsupported_spaces(env: gym.Env, observation_space: spaces.Space, act
+ 
+ def _check_nan(env: gym.Env) -> None:
+     """Check for Inf and NaN using the VecWrapper."""
++    if not torch_available:
++        return
+     vec_env = VecCheckNan(DummyVecEnv([lambda: env]))
+     for _ in range(10):
+         action = np.array([env.action_space.sample()])
+diff --git a/stable_baselines3/common/preprocessing.py b/stable_baselines3/common/preprocessing.py
+index 01422aa..0603891 100644
+--- stable_baselines3/common/preprocessing.py
++++ stable_baselines3/common/preprocessing.py
+@@ -1,10 +1,15 @@
++from ast import Import
+ import warnings
+ from typing import Dict, Tuple, Union
+ 
+ import numpy as np
+-import torch as th
+ from gym import spaces
+-from torch.nn import functional as F
++
++try:
++    import torch as th
++    from torch.nn import functional as F
++except ImportError:
++    pass  # Let any function calls that use torch fail naturally.
+ 
+ 
+ def is_image_space_channels_first(observation_space: spaces.Box) -> bool:
+@@ -83,10 +88,10 @@ def maybe_transpose(observation: np.ndarray, observation_space: spaces.Space) ->
+ 
+ 
+ def preprocess_obs(
+-    obs: th.Tensor,
++    obs,
+     observation_space: spaces.Space,
+     normalize_images: bool = True,
+-) -> Union[th.Tensor, Dict[str, th.Tensor]]:
++):
+     """
+     Preprocess observation to be to a neural network.
+     For images, it normalizes the values by dividing them by 255 (to have values in [0, 1])
+
diff --git a/tools/workspace/stable_baselines3_internal/package.BUILD.bazel b/tools/workspace/stable_baselines3_internal/package.BUILD.bazel
new file mode 100644
index 000000000000..f5fbe2d92184
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/package.BUILD.bazel
@@ -0,0 +1,14 @@
+# -*- python -*-
+
+load("@drake//tools/skylark:py.bzl", "py_library")
+
+licenses(["notice"])  # MIT
+
+# Internal vendoring of a few files of stable_baselines3; see README.md
+py_library(
+    name = "stable_baselines3",
+    srcs = glob(["**/*.py"]),
+    deps = ["@gym_py"],
+    data = glob(["**/version.txt"]),
+    visibility = ["//visibility:public"],
+)
diff --git a/tools/workspace/stable_baselines3_internal/repository.bzl b/tools/workspace/stable_baselines3_internal/repository.bzl
new file mode 100644
index 000000000000..4f98e74dbd44
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/repository.bzl
@@ -0,0 +1,19 @@
+# -*- python -*-
+
+load("@drake//tools/workspace:github.bzl", "github_archive")
+
+def stable_baselines3_internal_repository(
+        name,
+        mirrors = None):
+    github_archive(
+        name = name,
+        repository = "DLR-RM/stable-baselines3",
+        commit = "v1.6.0",
+        sha256 = "f6642fb002adf7ce10087319ea8e9a331d95d26f6558067339f26c84fc588bb6",  # noqa
+        build_file = ":package.BUILD.bazel",
+        patches = [
+            ":connection.patch",
+            ":no_torch.patch",
+        ],
+        mirrors = mirrors,
+    )
diff --git a/tools/workspace/stable_baselines3_internal/test/stable_baselines3_internal_test.py b/tools/workspace/stable_baselines3_internal/test/stable_baselines3_internal_test.py
new file mode 100644
index 000000000000..9ecb95925b2b
--- /dev/null
+++ b/tools/workspace/stable_baselines3_internal/test/stable_baselines3_internal_test.py
@@ -0,0 +1,9 @@
+import unittest
+
+
+class StableBaselines3InternalTest(unittest.TestCase):
+    """Test that the methods that we use in drake are able to be loaded
+    in spite of Drake not having all of SB3's dependencies."""
+    def test_import(self):
+        from stable_baselines3.common.env_checker import check_env
+        help(check_env)