[Frontend][Bugfix] allow using the default middleware with a root path (#3788)

Co-authored-by: A-Mahla <>

vllm/entrypoints/openai/api_server.py

@@ -127,7 +127,8 @@ if __name__ == "__main__":
 
         @app.middleware("http")
         async def authentication(request: Request, call_next):
-            if not request.url.path.startswith("/v1"):
+            root_path = "" if args.root_path is None else args.root_path
+            if not request.url.path.startswith(f"{root_path}/v1"):
                 return await call_next(request)
             if request.headers.get("Authorization") != "Bearer " + token:
                 return JSONResponse(content={"error": "Unauthorized"},