diff --git a/fastapi/routing.py b/fastapi/routing.py
index 4eec6d1c7d..32c5cf1043 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -2004,13 +2004,16 @@ class _FrontendStaticFiles(StaticFiles):
             return self.file_response(full_path, stat_result, scope)
 
         if self.fallback == "404.html" or (
-            self.fallback == "auto" and self._fallback_file_exists("404.html")
+            self.fallback == "auto" and await self._fallback_file_exists("404.html")
         ):
             return await self._fallback_response("404.html", scope, status_code=404)
 
         if (
             self.fallback == "index.html"
-            or (self.fallback == "auto" and self._fallback_file_exists("index.html"))
+            or (
+                self.fallback == "auto"
+                and await self._fallback_file_exists("index.html")
+            )
         ) and _is_frontend_navigation_request(scope):
             return await self._fallback_response("index.html", scope, status_code=200)
 
@@ -2043,8 +2046,8 @@ class _FrontendStaticFiles(StaticFiles):
                 return full_path, stat_result, True
         return None
 
-    def _fallback_file_exists(self, fallback: str) -> bool:
-        _, stat_result = self.lookup_path(fallback)
+    async def _fallback_file_exists(self, fallback: str) -> bool:
+        _, stat_result = await run_in_threadpool(self.lookup_path, fallback)
         return stat_result is not None and stat.S_ISREG(stat_result.st_mode)
 
     async def _fallback_response(
diff --git a/tests/test_frontend.py b/tests/test_frontend.py
index 0a44df72ed..eb380c8a50 100644
--- a/tests/test_frontend.py
+++ b/tests/test_frontend.py
@@ -1,3 +1,4 @@
+import asyncio
 import errno
 import os
 import runpy
@@ -775,11 +776,22 @@ def test_auto_fallback_prefers_404_over_index(tmp_path: Path):
     assert response.text == "missing"
 
 
-def test_auto_fallback_uses_index_when_404_is_missing(tmp_path: Path):
+def test_auto_fallback_uses_index_when_404_is_missing(monkeypatch, tmp_path: Path):
     dist = tmp_path / "dist"
     write_file(dist / "index.html", "app shell")
     app = FastAPI()
     app.frontend("/", directory=dist)
+    frontend_routes = app.router._frontend_routes
+    assert frontend_routes is not None
+    static_files = frontend_routes.routes[0].app
+    original_lookup_path = static_files.lookup_path
+
+    def lookup_path(path: str):
+        with pytest.raises(RuntimeError, match="no running event loop"):
+            asyncio.get_running_loop()
+        return original_lookup_path(path)
+
+    monkeypatch.setattr(static_files, "lookup_path", lookup_path)
 
     response = TestClient(app).get("/dashboard", headers={"accept": "text/html"})