diff --git a/django/db/migrations/loader.py b/django/db/migrations/loader.py
index 4147cc3f09..518212b6d0 100644
--- a/django/db/migrations/loader.py
+++ b/django/db/migrations/loader.py
@@ -97,7 +97,10 @@ class MigrationLoader:
                 if was_loaded:
                     reload(module)
             self.migrated_apps.add(app_config.label)
-            migration_names = {name for _, name, is_pkg in pkgutil.iter_modules(module.__path__) if not is_pkg}
+            migration_names = {
+                name for _, name, is_pkg in pkgutil.iter_modules(module.__path__)
+                if not is_pkg and name[0] not in '_~'
+            }
             # Load migrations
             for migration_name in migration_names:
                 migration_path = '%s.%s' % (module_name, migration_name)
diff --git a/docs/releases/2.1.2.txt b/docs/releases/2.1.2.txt
index 17c50fffd7..753b87a7fb 100644
--- a/docs/releases/2.1.2.txt
+++ b/docs/releases/2.1.2.txt
@@ -11,3 +11,6 @@ Bugfixes
 
 * Fixed a regression where nonexistent joins in ``F()`` no longer raised
   ``FieldError`` (:ticket:`29727`).
+
+* Fixed a regression where files starting with a tilde or underscore weren't
+  ignored by the migrations loader (:ticket:`29749`).
diff --git a/tests/migrations/test_loader.py b/tests/migrations/test_loader.py
index 71d3c9ca36..a7666c5c2d 100644
--- a/tests/migrations/test_loader.py
+++ b/tests/migrations/test_loader.py
@@ -500,6 +500,14 @@ class LoaderTests(TestCase):
         }
         self.assertEqual(plan, expected_plan)
 
+    @override_settings(MIGRATION_MODULES={'migrations': 'migrations.test_migrations_private'})
+    def test_ignore_files(self):
+        """Files prefixed with underscore, tilde, or dot aren't loaded."""
+        loader = MigrationLoader(connection)
+        loader.load_disk()
+        migrations = [name for app, name in loader.disk_migrations if app == 'migrations']
+        self.assertEqual(migrations, ['0001_initial'])
+
 
 class PycLoaderTests(MigrationTestBase):
 
diff --git a/tests/migrations/test_migrations_private/.util.py b/tests/migrations/test_migrations_private/.util.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/migrations/test_migrations_private/0001_initial.py b/tests/migrations/test_migrations_private/0001_initial.py
new file mode 100644
index 0000000000..bd613aa95e
--- /dev/null
+++ b/tests/migrations/test_migrations_private/0001_initial.py
@@ -0,0 +1,5 @@
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+    pass
diff --git a/tests/migrations/test_migrations_private/__init__.py b/tests/migrations/test_migrations_private/__init__.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/migrations/test_migrations_private/_util.py b/tests/migrations/test_migrations_private/_util.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/migrations/test_migrations_private/~util.py b/tests/migrations/test_migrations_private/~util.py
new file mode 100644
index 0000000000..e69de29bb2