diff --git a/news/6924.bugfix b/news/6924.bugfix
new file mode 100644
index 00000000000..d89652cba7b
--- /dev/null
+++ b/news/6924.bugfix
@@ -0,0 +1 @@
+Don't fail installation using pip.exe on Windows when pip wouldn't be upgraded.
diff --git a/src/pip/_internal/commands/install.py b/src/pip/_internal/commands/install.py
index bd8a2a26d8e..71e67068f2e 100644
--- a/src/pip/_internal/commands/install.py
+++ b/src/pip/_internal/commands/install.py
@@ -362,8 +362,16 @@ def run(self, options, args):
                     )
                     resolver.resolve(requirement_set)
 
+                    try:
+                        pip_req = requirement_set.get_requirement("pip")
+                    except KeyError:
+                        modifying_pip = None
+                    else:
+                        # If we're not replacing an already installed pip,
+                        # we're not modifying it.
+                        modifying_pip = pip_req.satisfied_by is None
                     protect_pip_from_modification_on_windows(
-                        modifying_pip=requirement_set.has_requirement("pip")
+                        modifying_pip=modifying_pip
                     )
 
                     # Consider legacy and PEP517-using requirements separately
diff --git a/src/pip/_internal/utils/misc.py b/src/pip/_internal/utils/misc.py
index d19df9459ac..b1e0b7f1bcc 100644
--- a/src/pip/_internal/utils/misc.py
+++ b/src/pip/_internal/utils/misc.py
@@ -1307,6 +1307,7 @@ def hide_url(url):
 
 
 def protect_pip_from_modification_on_windows(modifying_pip):
+    # type: (bool) -> None
     """Protection of pip.exe from modification on Windows
 
     On Windows, any operation modifying pip should be run as:
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index 27d8b8ef68b..06520fb1c2f 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1636,3 +1636,21 @@ def test_protect_pip_from_modification_via_sub_deps_on_windows(script):
         .format(' '.join(new_command))
     )
     assert expected_message in result.stderr, str(result)
+
+
+@pytest.mark.parametrize(
+    'install_args, expected_message', [
+        ([], 'Requirement already satisfied: pip in'),
+        (['--upgrade'], 'Requirement already up-to-date: pip in'),
+    ]
+)
+@pytest.mark.parametrize("use_module", [True, False])
+def test_install_pip_does_not_modify_pip_when_satisfied(
+        script, install_args, expected_message, use_module):
+    """
+    Test it doesn't upgrade the pip if it already satisfies the requirement.
+    """
+    result = script.pip_install_local(
+        'pip', *install_args, use_module=use_module
+    )
+    assert expected_message in result.stdout, str(result)