diff --git a/fastapi/_compat/v2.py b/fastapi/_compat/v2.py
index 5cd49343b..7196a6190 100644
--- a/fastapi/_compat/v2.py
+++ b/fastapi/_compat/v2.py
@@ -304,7 +304,7 @@ def _remap_definitions_and_field_mappings(
     old_name_to_new_name_map = {}
     for field_key, schema in field_mapping.items():
         model = field_key[0].type_
-        if model not in model_name_map:
+        if model not in model_name_map or "$ref" not in schema:
             continue
         new_name = model_name_map[model]
         old_name = schema["$ref"].split("/")[-1]