diff --git a/fastapi/applications.py b/fastapi/applications.py
index d6148b9d5..f44f52ed3 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -979,15 +979,18 @@ class FastAPI(Starlette):
 
         if ignore_trailing_slash:
 
-            def ignore_trailing_whitespace_middleware(app):
-                async def ignore_trailing_whitespace_wrapper(scope, receive, send):
+            class _IgnoreTrailingWhitespaceMiddleware:
+                def __init__(self, app: ASGIApp):
+                    self.app = app
+
+                async def __call__(
+                    self, scope: Scope, receive: Receive, send: Send
+                ) -> None:
                     if scope["type"] in {"http", "websocket"}:
                         scope["path"] = scope["path"].rstrip("/")
-                    await app(scope, receive, send)
-
-                return ignore_trailing_whitespace_wrapper
+                    await self.app(scope, receive, send)
 
-            self.add_middleware(ignore_trailing_whitespace_middleware)
+            self.add_middleware(_IgnoreTrailingWhitespaceMiddleware)
 
         self.setup()
 
diff --git a/fastapi/routing.py b/fastapi/routing.py
index 0935a29f2..b06704574 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -1293,10 +1293,10 @@ class APIRouter(routing.Router):
         if responses is None:
             responses = {}
         for route in router.routes:
-            path = route.path
-            if self.ignore_trailing_slash:
-                path = path.rstrip("/")
             if isinstance(route, APIRoute):
+                path = route.path
+                if self.ignore_trailing_slash:
+                    path = path.rstrip("/")
                 combined_responses = {**responses, **route.responses}
                 use_response_class = get_value_or_default(
                     route.response_class,
@@ -1356,6 +1356,9 @@ class APIRouter(routing.Router):
                     generate_unique_id_function=current_generate_unique_id,
                 )
             elif isinstance(route, routing.Route):
+                path = route.path
+                if self.ignore_trailing_slash:
+                    path = path.rstrip("/")
                 methods = list(route.methods or [])
                 self.add_route(
                     prefix + path,
@@ -1365,6 +1368,9 @@ class APIRouter(routing.Router):
                     name=route.name,
                 )
             elif isinstance(route, APIWebSocketRoute):
+                path = route.path
+                if self.ignore_trailing_slash:
+                    path = path.rstrip("/")
                 current_dependencies = []
                 if dependencies:
                     current_dependencies.extend(dependencies)
@@ -1377,6 +1383,9 @@ class APIRouter(routing.Router):
                     name=route.name,
                 )
             elif isinstance(route, routing.WebSocketRoute):
+                path = route.path
+                if self.ignore_trailing_slash:
+                    path = path.rstrip("/")
                 self.add_websocket_route(prefix + path, route.endpoint, name=route.name)
         for handler in router.on_startup:
             self.add_event_handler("startup", handler)