diff --git a/django/apps/registry.py b/django/apps/registry.py
index 62650ca4bc..268e1a6af7 100644
--- a/django/apps/registry.py
+++ b/django/apps/registry.py
@@ -286,13 +286,14 @@ class Apps:
         change after Django has loaded the settings, there is no reason to get
         the respective settings attribute over and over again.
         """
+        to_string = to_string.lower()
         for model in self.get_models(include_swapped=True):
             swapped = model._meta.swapped
             # Is this model swapped out for the model given by to_string?
-            if swapped and swapped == to_string:
+            if swapped and swapped.lower() == to_string:
                 return model._meta.swappable
             # Is this model swappable and the one given by to_string?
-            if model._meta.swappable and model._meta.label == to_string:
+            if model._meta.swappable and model._meta.label_lower == to_string:
                 return model._meta.swappable
         return None
 
diff --git a/docs/releases/4.0.1.txt b/docs/releases/4.0.1.txt
index 50c84bfe17..5fea7aa8df 100644
--- a/docs/releases/4.0.1.txt
+++ b/docs/releases/4.0.1.txt
@@ -19,3 +19,7 @@ Bugfixes
 * Relaxed the check added in Django 4.0 to reallow use of a duck-typed
   ``HttpRequest`` in ``django.views.decorators.cache.cache_control()`` and
   ``never_cache()`` decorators (:ticket:`33350`).
+
+* Fixed a regression in Django 4.0 that caused creating bogus migrations for
+  models that reference swappable models such as ``auth.User``
+  (:ticket:`33366`).
diff --git a/tests/field_deconstruction/tests.py b/tests/field_deconstruction/tests.py
index b2fb097100..70846f23d3 100644
--- a/tests/field_deconstruction/tests.py
+++ b/tests/field_deconstruction/tests.py
@@ -211,6 +211,13 @@ class FieldDeconstructionTests(SimpleTestCase):
         self.assertEqual(args, [])
         self.assertEqual(kwargs, {"to": "auth.user", "on_delete": models.CASCADE})
         self.assertEqual(kwargs['to'].setting_name, "AUTH_USER_MODEL")
+        # Swap detection for lowercase swappable model.
+        field = models.ForeignKey('auth.user', models.CASCADE)
+        name, path, args, kwargs = field.deconstruct()
+        self.assertEqual(path, 'django.db.models.ForeignKey')
+        self.assertEqual(args, [])
+        self.assertEqual(kwargs, {'to': 'auth.user', 'on_delete': models.CASCADE})
+        self.assertEqual(kwargs['to'].setting_name, 'AUTH_USER_MODEL')
         # Test nonexistent (for now) model
         field = models.ForeignKey("something.Else", models.CASCADE)
         name, path, args, kwargs = field.deconstruct()
@@ -273,6 +280,19 @@ class FieldDeconstructionTests(SimpleTestCase):
         self.assertEqual(kwargs, {"to": "auth.permission", "on_delete": models.CASCADE})
         self.assertEqual(kwargs['to'].setting_name, "AUTH_USER_MODEL")
 
+        # Model names are case-insensitive.
+        with isolate_lru_cache(apps.get_swappable_settings_name):
+            # It doesn't matter that we swapped out user for permission;
+            # there's no validation. We just want to check the setting stuff
+            # works.
+            field = models.ForeignKey('auth.permission', models.CASCADE)
+            name, path, args, kwargs = field.deconstruct()
+
+        self.assertEqual(path, 'django.db.models.ForeignKey')
+        self.assertEqual(args, [])
+        self.assertEqual(kwargs, {'to': 'auth.permission', 'on_delete': models.CASCADE})
+        self.assertEqual(kwargs['to'].setting_name, 'AUTH_USER_MODEL')
+
     def test_one_to_one(self):
         # Test basic pointing
         from django.contrib.auth.models import Permission
diff --git a/tests/migrations/test_autodetector.py b/tests/migrations/test_autodetector.py
index 18055f242b..d25b14cedb 100644
--- a/tests/migrations/test_autodetector.py
+++ b/tests/migrations/test_autodetector.py
@@ -1965,6 +1965,22 @@ class AutodetectorTests(TestCase):
         self.assertOperationAttributes(changes, 'testapp', 0, 0, name="Author")
         self.assertMigrationDependencies(changes, 'testapp', 0, [("__setting__", "AUTH_USER_MODEL")])
 
+    def test_swappable_lowercase(self):
+        model_state = ModelState('testapp', 'Document', [
+            ('id', models.AutoField(primary_key=True)),
+            ('owner', models.ForeignKey(
+                settings.AUTH_USER_MODEL.lower(), models.CASCADE,
+            )),
+        ])
+        with isolate_lru_cache(apps.get_swappable_settings_name):
+            changes = self.get_changes([], [model_state])
+        self.assertNumberMigrations(changes, 'testapp', 1)
+        self.assertOperationTypes(changes, 'testapp', 0, ['CreateModel'])
+        self.assertOperationAttributes(changes, 'testapp', 0, 0, name='Document')
+        self.assertMigrationDependencies(
+            changes, 'testapp', 0, [('__setting__', 'AUTH_USER_MODEL')],
+        )
+
     def test_swappable_changed(self):
         with isolate_lru_cache(apps.get_swappable_settings_name):
             before = self.make_project_state([self.custom_user, self.author_with_user])