diff --git a/starlette/responses.py b/starlette/responses.py
index 31874f655..a82fdb21a 100644
--- a/starlette/responses.py
+++ b/starlette/responses.py
@@ -341,7 +341,7 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
                 stat_result = await anyio.to_thread.run_sync(os.stat, self.path)
                 self.set_stat_headers(stat_result)
             except FileNotFoundError:
-                raise RuntimeError(f"File at path {self.path} does not exist.")
+                pass
             else:
                 mode = stat_result.st_mode
                 if not stat.S_ISREG(mode):
diff --git a/tests/test_responses.py b/tests/test_responses.py
index d5ed83499..20bcc8775 100644
--- a/tests/test_responses.py
+++ b/tests/test_responses.py
@@ -299,9 +299,8 @@ def test_file_response_with_missing_file_raises_error(tmp_path: Path, test_clien
     path = tmp_path / "404.txt"
     app = FileResponse(path=path, filename="404.txt")
     client = test_client_factory(app)
-    with pytest.raises(RuntimeError) as exc_info:
+    with pytest.raises(FileNotFoundError):
         client.get("/")
-    assert "does not exist" in str(exc_info.value)
 
 
 def test_file_response_with_chinese_filename(tmp_path: Path, test_client_factory: TestClientFactory) -> None: