diff --git a/django/db/migrations/operations/models.py b/django/db/migrations/operations/models.py
index ef7ecf3184..b929367bce 100644
--- a/django/db/migrations/operations/models.py
+++ b/django/db/migrations/operations/models.py
@@ -772,11 +772,13 @@ class AddIndex(IndexOperation):
 
     def database_forwards(self, app_label, schema_editor, from_state, to_state):
         model = to_state.apps.get_model(app_label, self.model_name)
-        schema_editor.add_index(model, self.index)
+        if self.allow_migrate_model(schema_editor.connection.alias, model):
+            schema_editor.add_index(model, self.index)
 
     def database_backwards(self, app_label, schema_editor, from_state, to_state):
         model = from_state.apps.get_model(app_label, self.model_name)
-        schema_editor.remove_index(model, self.index)
+        if self.allow_migrate_model(schema_editor.connection.alias, model):
+            schema_editor.remove_index(model, self.index)
 
     def deconstruct(self):
         kwargs = {
@@ -812,15 +814,17 @@ class RemoveIndex(IndexOperation):
 
     def database_forwards(self, app_label, schema_editor, from_state, to_state):
         model = from_state.apps.get_model(app_label, self.model_name)
-        from_model_state = from_state.models[app_label, self.model_name_lower]
-        index = from_model_state.get_index_by_name(self.name)
-        schema_editor.remove_index(model, index)
+        if self.allow_migrate_model(schema_editor.connection.alias, model):
+            from_model_state = from_state.models[app_label, self.model_name_lower]
+            index = from_model_state.get_index_by_name(self.name)
+            schema_editor.remove_index(model, index)
 
     def database_backwards(self, app_label, schema_editor, from_state, to_state):
         model = to_state.apps.get_model(app_label, self.model_name)
-        to_model_state = to_state.models[app_label, self.model_name_lower]
-        index = to_model_state.get_index_by_name(self.name)
-        schema_editor.add_index(model, index)
+        if self.allow_migrate_model(schema_editor.connection.alias, model):
+            to_model_state = to_state.models[app_label, self.model_name_lower]
+            index = to_model_state.get_index_by_name(self.name)
+            schema_editor.add_index(model, index)
 
     def deconstruct(self):
         kwargs = {
diff --git a/tests/migrations/test_operations.py b/tests/migrations/test_operations.py
index 0d2a6ea9bd..743bcd81a4 100644
--- a/tests/migrations/test_operations.py
+++ b/tests/migrations/test_operations.py
@@ -2347,3 +2347,21 @@ class SwappableOperationTests(OperationTestBase):
         with connection.schema_editor() as editor:
             operation.database_backwards("test_adfligsw", editor, new_state, project_state)
         self.assertTableNotExists("test_adfligsw_pony")
+
+    @override_settings(TEST_SWAP_MODEL='migrations.SomeFakeModel')
+    def test_indexes_ignore_swapped(self):
+        """
+        Add/RemoveIndex operations ignore swapped models.
+        """
+        operation = migrations.AddIndex('Pony', models.Index(fields=['pink'], name='my_name_idx'))
+        project_state, new_state = self.make_test_state('test_adinigsw', operation)
+        with connection.schema_editor() as editor:
+            # No database queries should be run for swapped models
+            operation.database_forwards('test_adinigsw', editor, project_state, new_state)
+            operation.database_backwards('test_adinigsw', editor, new_state, project_state)
+
+        operation = migrations.RemoveIndex('Pony', models.Index(fields=['pink'], name='my_name_idx'))
+        project_state, new_state = self.make_test_state("test_rminigsw", operation)
+        with connection.schema_editor() as editor:
+            operation.database_forwards('test_rminigsw', editor, project_state, new_state)
+            operation.database_backwards('test_rminigsw', editor, new_state, project_state)