diff --git a/src/datamodel_code_generator/parser/jsonschema.py b/src/datamodel_code_generator/parser/jsonschema.py
index 472d26f66..ab7687079 100644
--- a/src/datamodel_code_generator/parser/jsonschema.py
+++ b/src/datamodel_code_generator/parser/jsonschema.py
@@ -460,14 +460,19 @@ def has_ref_with_schema_keywords(self) -> bool:
         """Check if schema has $ref combined with schema-affecting keywords.
 
         Metadata-only keywords (title, description, etc.) are excluded
-        as they don't affect the schema structure.
+        as they don't affect the schema structure. OpenAPI/JSON Schema
+        extension fields (x-*) are also excluded as they are vendor
+        extensions and don't affect the core schema structure.
         """
         if not self.ref:
             return False
         other_fields = get_fields_set(self) - {"ref"}
         schema_affecting_fields = other_fields - self.__metadata_only_fields__ - {"extras"}
         if self.extras:
-            schema_affecting_extras = {k for k in self.extras if k not in self.__metadata_only_fields__}
+            # Filter out metadata-only fields AND extension fields (x-* prefix)
+            schema_affecting_extras = {
+                k for k in self.extras if k not in self.__metadata_only_fields__ and not k.startswith("x-")
+            }
             if schema_affecting_extras:
                 schema_affecting_fields |= {"extras"}
         return bool(schema_affecting_fields)
diff --git a/tests/parser/test_jsonschema.py b/tests/parser/test_jsonschema.py
index 4452dce3c..5bb7efea7 100644
--- a/tests/parser/test_jsonschema.py
+++ b/tests/parser/test_jsonschema.py
@@ -915,6 +915,31 @@ def test_has_ref_with_schema_keywords_extras_with_metadata_only_keys() -> None:
     assert obj.has_ref_with_schema_keywords is False
 
 
+def test_has_ref_with_schema_keywords_extras_with_extension_keys() -> None:
+    """Test has_ref_with_schema_keywords when extras contains only x-* extension keys.
+
+    OpenAPI/JSON Schema extension fields (x-*) should be treated as metadata
+    and not trigger schema merging, which prevents infinite recursion with
+    self-referencing schemas.
+    """
+    # x-* extensions are vendor extensions, should not trigger merge
+    obj = model_validate(
+        JsonSchemaObject,
+        {
+            "$ref": "#/$defs/Base",
+            "deprecated": False,  # metadata-only field
+            "x-internalAPI": False,  # extension field
+            "x-custom-field": "value",  # another extension field
+        },
+    )
+    # Verify extras contains extension keys
+    assert obj.extras
+    assert "x-internalAPI" in obj.extras
+    assert "x-custom-field" in obj.extras
+    # Extension fields should NOT trigger schema merge
+    assert obj.has_ref_with_schema_keywords is False
+
+
 def test_has_ref_with_schema_keywords_no_extras() -> None:
     """Test has_ref_with_schema_keywords when extras is empty."""
     # Only $ref and a schema-affecting field, no extras