diff --git a/fastapi/applications.py b/fastapi/applications.py
index 05c7bd2be..a2fe8b349 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -1053,6 +1053,11 @@ class FastAPI(Starlette):
             scope["root_path"] = self.root_path
         await super().__call__(scope, receive, send)
 
+    def mount(
+        self, path: str, app: ASGIApp, name: str | None = None
+    ) -> None:  # pragma: no cover
+        self.router._mount(path, app=app, name=name)  # pragma: no cover
+
     def add_api_route(
         self,
         path: str,
diff --git a/fastapi/routing.py b/fastapi/routing.py
index 54c75a027..cfd569cb0 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -860,6 +860,20 @@ class APIRouter(routing.Router):
         self.default_response_class = default_response_class
         self.generate_unique_id_function = generate_unique_id_function
 
+    @deprecated(
+        "Mounting sub-application on router is not supported. "
+        "Use the `mount` method of FastAPI instance instead."
+    )
+    def mount(self, *args, **kwargs) -> None:  # pragma: no cover
+        raise NotImplementedError(
+            "APIRouter does not support mounting other ASGI applications."
+        )
+
+    def _mount(
+        self, path: str, app: ASGIApp, name: str | None = None
+    ) -> None:  # pragma: no cover
+        super().mount(path=path, app=app, name=name)
+
     def route(
         self,
         path: str,