diff --git a/src/py_avro_schema/_schemas.py b/src/py_avro_schema/_schemas.py
index ecaa150..7eb04a9 100644
--- a/src/py_avro_schema/_schemas.py
+++ b/src/py_avro_schema/_schemas.py
@@ -312,14 +312,20 @@ def _wrap_as_record(self, inner_schema: JSONObj, names: NamesType) -> JSONType:
         if fullname in names:
             return fullname
         names.append(fullname)
+
+        fields = [
+            {"name": REF_ID_KEY, "type": ["null", "long"], "default": None},
+            {"name": REF_DATA_KEY, "type": inner_schema},
+        ]
+        if Option.ADD_RUNTIME_TYPE_FIELD in self.options:
+            fields.append({"name": RUNTIME_TYPE_KEY, "type": ["null", "string"]})
+
         record_schema = {
             "type": "record",
             "name": record_name,
-            "fields": [
-                {"name": REF_ID_KEY, "type": ["null", "long"], "default": None},
-                {"name": REF_DATA_KEY, "type": inner_schema},
-            ],
+            "fields": fields,
         }
+
         if self.namespace:
             record_schema["namespace"] = self.namespace
         return record_schema
diff --git a/tests/test_avro_schema.py b/tests/test_avro_schema.py
index 5bffbcb..691e990 100644
--- a/tests/test_avro_schema.py
+++ b/tests/test_avro_schema.py
@@ -80,3 +80,17 @@ class PyType:
         ],
     }
     assert_schema(PyType, expected, options=pas.Option.ADD_RUNTIME_TYPE_FIELD)
+
+
+def test_add_type_field_on_wrapped_record():
+    py_type = list[str]
+    expected = {
+        "type": "record",
+        "name": "StrList",
+        "fields": [
+            {"name": "__id", "type": ["null", "long"], "default": None},
+            {"name": "__data", "type": {"type": "array", "items": "string"}},
+            {"name": "_runtime_type", "type": ["null", "string"]},
+        ],
+    }
+    assert_schema(py_type, expected, options=pas.Option.WRAP_INTO_RECORDS | pas.Option.ADD_RUNTIME_TYPE_FIELD)