diff --git a/.changelog/37832.txt b/.changelog/37832.txt
new file mode 100644
index 00000000000..17c1caf4c51
--- /dev/null
+++ b/.changelog/37832.txt
@@ -0,0 +1,3 @@
+```release-note:bug
+resource/aws_ssm_parameter: Fix `Cannot import non-existent remote object` errors when importing resources with version
+```
\ No newline at end of file
diff --git a/internal/service/ssm/parameter.go b/internal/service/ssm/parameter.go
index 7fd23f6b575..86e3f7debaa 100644
--- a/internal/service/ssm/parameter.go
+++ b/internal/service/ssm/parameter.go
@@ -257,7 +257,7 @@ func resourceParameterRead(ctx context.Context, d *schema.ResourceData, meta int
 		return sdkdiag.AppendErrorf(diags, "invalid configuration, cannot set type = %s and insecure_value", param.Type)
 	}
 
-	detail, err := findParameterMetadataByName(ctx, conn, d.Id())
+	detail, err := findParameterMetadataByName(ctx, conn, d.Get(names.AttrName).(string))
 
 	if !d.IsNewResource() && tfresource.NotFound(err) {
 		log.Printf("[WARN] SSM Parameter %s not found, removing from state", d.Id())
diff --git a/internal/service/ssm/parameter_test.go b/internal/service/ssm/parameter_test.go
index e2afdf86e0b..b12e6a78411 100644
--- a/internal/service/ssm/parameter_test.go
+++ b/internal/service/ssm/parameter_test.go
@@ -54,6 +54,16 @@ func TestAccSSMParameter_basic(t *testing.T) {
 				ImportStateVerify:       true,
 				ImportStateVerifyIgnore: []string{"overwrite"},
 			},
+			// Test import with version.
+			// https://github.com/hashicorp/terraform-provider-aws/issues/37812.
+			{
+				ResourceName:                         resourceName,
+				ImportState:                          true,
+				ImportStateId:                        name + ":1",
+				ImportStateVerify:                    true,
+				ImportStateVerifyIdentifierAttribute: names.AttrName,
+				ImportStateVerifyIgnore:              []string{names.AttrID, "overwrite"},
+			},
 		},
 	})
 }