diff --git a/django/db/backends/base/schema.py b/django/db/backends/base/schema.py
index 663e03dafef..c9dff6b61f3 100644
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -1013,11 +1013,13 @@ class BaseDatabaseSchemaEditor:
         )
 
     def _create_unique_sql(self, model, columns):
+        def create_unique_name(*args, **kwargs):
+            return self.quote_name(self._create_index_name(*args, **kwargs))
         table = model._meta.db_table
         return Statement(
             self.sql_create_unique,
             table=Table(table, self.quote_name),
-            name=IndexName(table, columns, '_uniq', self._create_index_name),
+            name=IndexName(table, columns, '_uniq', create_unique_name),
             columns=Columns(table, columns, self.quote_name),
         )
 
diff --git a/docs/releases/2.1.2.txt b/docs/releases/2.1.2.txt
index 3118df77ae4..3651440bc6e 100644
--- a/docs/releases/2.1.2.txt
+++ b/docs/releases/2.1.2.txt
@@ -19,3 +19,6 @@ Bugfixes
   (:ticket:`29755`).
 
 * Added compatibility for ``cx_Oracle`` 7 (:ticket:`29759`).
+
+* Fixed a regression in Django 2.0 where unique index names weren't quoted
+  (:ticket:`29778`).
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index f18b68d04d8..245d4b09185 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -1558,6 +1558,18 @@ class SchemaTests(TransactionTestCase):
             TagUniqueRename.objects.create(title="bar", slug2="foo")
         Tag.objects.all().delete()
 
+    def test_unique_name_quoting(self):
+        old_table_name = TagUniqueRename._meta.db_table
+        try:
+            with connection.schema_editor() as editor:
+                editor.create_model(TagUniqueRename)
+                editor.alter_db_table(TagUniqueRename, old_table_name, 'unique-table')
+                TagUniqueRename._meta.db_table = 'unique-table'
+                # This fails if the unique index name isn't quoted.
+                editor.alter_unique_together(TagUniqueRename, [], (('title', 'slug2'),))
+        finally:
+            TagUniqueRename._meta.db_table = old_table_name
+
     @isolate_apps('schema')
     @unittest.skipIf(connection.vendor == 'sqlite', 'SQLite naively remakes the table on field alteration.')
     @skipUnlessDBFeature('supports_foreign_keys')