diff --git a/django/contrib/postgres/operations.py b/django/contrib/postgres/operations.py
index 12c850a073..0bb131ddf2 100644
--- a/django/contrib/postgres/operations.py
+++ b/django/contrib/postgres/operations.py
@@ -1,7 +1,7 @@
 from django.contrib.postgres.signals import (
     get_citext_oids, get_hstore_oids, register_type_handlers,
 )
-from django.db import NotSupportedError
+from django.db import NotSupportedError, router
 from django.db.migrations import AddIndex, RemoveIndex
 from django.db.migrations.operations.base import Operation
 
@@ -16,7 +16,10 @@ class CreateExtension(Operation):
         pass
 
     def database_forwards(self, app_label, schema_editor, from_state, to_state):
-        if schema_editor.connection.vendor != 'postgresql':
+        if (
+            schema_editor.connection.vendor != 'postgresql' or
+            not router.allow_migrate(schema_editor.connection.alias, app_label)
+        ):
             return
         schema_editor.execute("CREATE EXTENSION IF NOT EXISTS %s" % schema_editor.quote_name(self.name))
         # Clear cached, stale oids.
@@ -28,6 +31,8 @@ class CreateExtension(Operation):
         register_type_handlers(schema_editor.connection)
 
     def database_backwards(self, app_label, schema_editor, from_state, to_state):
+        if not router.allow_migrate(schema_editor.connection.alias, app_label):
+            return
         schema_editor.execute("DROP EXTENSION %s" % schema_editor.quote_name(self.name))
         # Clear cached, stale oids.
         get_hstore_oids.cache_clear()
diff --git a/tests/postgres_tests/test_operations.py b/tests/postgres_tests/test_operations.py
index 95c88d5fe0..7bcf6b2300 100644
--- a/tests/postgres_tests/test_operations.py
+++ b/tests/postgres_tests/test_operations.py
@@ -3,12 +3,16 @@ import unittest
 from migrations.test_base import OperationTestBase
 
 from django.db import NotSupportedError, connection
+from django.db.migrations.state import ProjectState
 from django.db.models import Index
-from django.test import modify_settings
+from django.test import modify_settings, override_settings
+from django.test.utils import CaptureQueriesContext
+
+from . import PostgreSQLTestCase
 
 try:
     from django.contrib.postgres.operations import (
-        AddIndexConcurrently, RemoveIndexConcurrently,
+        AddIndexConcurrently, CreateExtension, RemoveIndexConcurrently,
     )
     from django.contrib.postgres.indexes import BrinIndex, BTreeIndex
 except ImportError:
@@ -141,3 +145,44 @@ class RemoveIndexConcurrentlyTests(OperationTestBase):
         self.assertEqual(name, 'RemoveIndexConcurrently')
         self.assertEqual(args, [])
         self.assertEqual(kwargs, {'model_name': 'Pony', 'name': 'pony_pink_idx'})
+
+
+class NoExtensionRouter():
+    def allow_migrate(self, db, app_label, **hints):
+        return False
+
+
+@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL specific tests.')
+class CreateExtensionTests(PostgreSQLTestCase):
+    app_label = 'test_allow_create_extention'
+
+    @override_settings(DATABASE_ROUTERS=[NoExtensionRouter()])
+    def test_no_allow_migrate(self):
+        operation = CreateExtension('uuid-ossp')
+        project_state = ProjectState()
+        new_state = project_state.clone()
+        # Don't create an extension.
+        with CaptureQueriesContext(connection) as captured_queries:
+            with connection.schema_editor(atomic=False) as editor:
+                operation.database_forwards(self.app_label, editor, project_state, new_state)
+        self.assertEqual(len(captured_queries), 0)
+        # Reversal.
+        with CaptureQueriesContext(connection) as captured_queries:
+            with connection.schema_editor(atomic=False) as editor:
+                operation.database_backwards(self.app_label, editor, new_state, project_state)
+        self.assertEqual(len(captured_queries), 0)
+
+    def test_allow_migrate(self):
+        operation = CreateExtension('uuid-ossp')
+        project_state = ProjectState()
+        new_state = project_state.clone()
+        # Create an extension.
+        with CaptureQueriesContext(connection) as captured_queries:
+            with connection.schema_editor(atomic=False) as editor:
+                operation.database_forwards(self.app_label, editor, project_state, new_state)
+        self.assertIn('CREATE EXTENSION', captured_queries[0]['sql'])
+        # Reversal.
+        with CaptureQueriesContext(connection) as captured_queries:
+            with connection.schema_editor(atomic=False) as editor:
+                operation.database_backwards(self.app_label, editor, new_state, project_state)
+        self.assertIn('DROP EXTENSION', captured_queries[0]['sql'])