diff --git a/fastapi/applications.py b/fastapi/applications.py
index 5a7170dd6..480d03ab8 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -814,6 +814,13 @@ class FastAPI(Starlette):
             bool,
             Doc(
                 """
+                To ignore (or not) trailing slashes at the end of URIs.
+
+                For example, by setting `ignore_trailing_slash` to True,
+                requests to `/auth` and `/auth/` will have the same behaviour.
+
+                By default (`ignore_trailing_slash` is False), the two requests are treated differently.
+                One of them will result in a 307-redirect.
                 """
             ),
         ] = False,
@@ -973,7 +980,8 @@ class FastAPI(Starlette):
         if ignore_trailing_slash:
             def ignore_trailing_whitespace_middleware(app):
                 async def ignore_trailing_whitespace_wrapper(scope, receive, send):
-                    scope["path"] = scope["path"].rstrip("/")
+                    if scope["type"] in {"http", "websocket"}:
+                        scope["path"] = scope["path"].rstrip("/")
                     await app(scope, receive, send)
                 return ignore_trailing_whitespace_wrapper
             self.add_middleware(ignore_trailing_whitespace_middleware)
diff --git a/fastapi/routing.py b/fastapi/routing.py
index d59701ef5..2b68cb0d1 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -815,6 +815,13 @@ class APIRouter(routing.Router):
             bool,
             Doc(
                 """
+                To ignore (or not) trailing slashes at the end of URIs.
+
+                For example, by setting `ignore_trailing_slash` to True,
+                requests to `/auth` and `/auth/` will have the same behaviour.
+
+                By default (`ignore_trailing_slash` is False), the two requests are treated differently.
+                One of them will result in a 307-redirect.
                 """
             ),
         ] = False,
diff --git a/tests/test_ignore_trailing_slash.py b/tests/test_ignore_trailing_slash.py
index 16537d328..8cd3c802a 100644
--- a/tests/test_ignore_trailing_slash.py
+++ b/tests/test_ignore_trailing_slash.py
@@ -8,38 +8,52 @@ router = APIRouter()
 async def example_endpoint():
     return {"msg": "Example"}
 
+@app.get("/example2/")
+async def example_endpoint():
+    return {"msg": "Example 2"}
+
 @app.websocket("/websocket")
 async def websocket_endpoint(websocket: WebSocket):
     await websocket.accept()
     await websocket.send_text("Websocket")
     await websocket.close()
 
+@app.websocket("/websocket2/")
+async def websocket_endpoint(websocket: WebSocket):
+    await websocket.accept()
+    await websocket.send_text("Websocket 2")
+    await websocket.close()
+
 @router.get("/example")
 def route_endpoint():
     return {"msg": "Routing Example"}
 
+@router.get("/example2/")
+def route_endpoint():
+    return {"msg": "Routing Example 2"}
+
 app.include_router(router, prefix="/router")
 
 client = TestClient(app)
 
 def test_ignoring_trailing_slash():
-    response = client.get("/example", follow_redirects=False)
-    assert response.status_code == 200
-    assert response.json()["msg"] == "Example"
     response = client.get("/example/", follow_redirects=False)
     assert response.status_code == 200
     assert response.json()["msg"] == "Example"
+    response = client.get("/example2", follow_redirects=False)
+    assert response.status_code == 200
+    assert response.json()["msg"] == "Example 2"
 
 def test_ignoring_trailing_shlash_ws():
-    with client.websocket_connect("/websocket") as websocket:
-        assert websocket.receive_text() == "Websocket"
     with client.websocket_connect("/websocket/") as websocket:
         assert websocket.receive_text() == "Websocket"
+    with client.websocket_connect("/websocket2") as websocket:
+        assert websocket.receive_text() == "Websocket 2"
 
 def test_ignoring_trailing_routing():
-    response = client.get("router/example", follow_redirects=False)
-    assert response.status_code == 200
-    assert response.json()["msg"] == "Routing Example"
     response = client.get("router/example/", follow_redirects=False)
     assert response.status_code == 200
     assert response.json()["msg"] == "Routing Example"
+    response = client.get("router/example2", follow_redirects=False)
+    assert response.status_code == 200
+    assert response.json()["msg"] == "Routing Example 2"
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