diff --git a/fastapi/applications.py b/fastapi/applications.py
index 41d86143e..a2fc33f0e 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -1133,6 +1133,11 @@ 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:
+        self.router._mount(path, app=app, name=name)
+
+
     def add_api_route(
         self,
         path: str,
diff --git a/fastapi/routing.py b/fastapi/routing.py
index ea82ab14a..f5db323cb 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -74,6 +74,7 @@ from starlette.routing import (
     get_name,
 )
 from starlette.routing import Mount as Mount  # noqa
+from starlette.staticfiles import StaticFiles
 from starlette.types import AppType, ASGIApp, Lifespan, Receive, Scope, Send
 from starlette.websockets import WebSocket
 from typing_extensions import deprecated
@@ -993,6 +994,20 @@ class APIRouter(routing.Router):
         self.default_response_class = default_response_class
         self.generate_unique_id_function = generate_unique_id_function
 
+    def mount(self, path: str, app: ASGIApp, name: str | None = None) -> None:
+        """
+        Mount a StaticFiles instance.
+        Will raise a FastAPIError exception if app is not an instance of StaticFiles.
+        """
+        if not isinstance(app, StaticFiles):
+            raise FastAPIError(
+                "APIRouter does not support mounting ASGI applications other than StaticFiles."
+            )
+        self._mount(path=path, app=app, name=name)
+
+    def _mount(self, path: str, app: ASGIApp, name: str | None = None) -> None:
+        super().mount(path=path, app=app, name=name)
+
     def route(
         self,
         path: str,
@@ -1489,6 +1504,11 @@ class APIRouter(routing.Router):
                 self.add_websocket_route(
                     prefix + route.path, route.endpoint, name=route.name
                 )
+            elif (  # fmt: skip
+                isinstance(route, routing.Mount) and isinstance(route.app, StaticFiles)
+            ):
+                self.mount(prefix + route.path, route.app, name=route.name)
+
         for handler in router.on_startup:
             self.add_event_handler("startup", handler)
         for handler in router.on_shutdown:
diff --git a/tests/test_apirouter_mount.py b/tests/test_apirouter_mount.py
new file mode 100644
index 000000000..a873cfa49
--- /dev/null
+++ b/tests/test_apirouter_mount.py
@@ -0,0 +1,32 @@
+import pytest
+from fastapi import APIRouter, FastAPI
+from fastapi.exceptions import FastAPIError
+from fastapi.staticfiles import StaticFiles
+from fastapi.testclient import TestClient
+
+
+def test_mount_static_files_to_apirouter(tmp_path):
+    static_asset = tmp_path / "index.html"
+    static_asset.write_text("Hello, World!")
+
+    router = APIRouter()
+    router.mount("/static", StaticFiles(directory=tmp_path), name="static")
+
+    app = FastAPI()
+    app.include_router(router)
+
+    client = TestClient(app)
+    response = client.get("/static/index.html")
+    assert response.status_code == 200
+    assert response.text == "Hello, World!"
+
+
+def test_mount_app_to_apirouter_raises():
+    router = APIRouter()
+    sub_app = FastAPI()
+
+    with pytest.raises(
+        FastAPIError,
+        match="APIRouter does not support mounting ASGI applications other than StaticFiles.",
+    ):
+        router.mount("/sub", sub_app)