diff --git a/fastapi/openapi/utils.py b/fastapi/openapi/utils.py
index 808646cc2..ca1d5a632 100644
--- a/fastapi/openapi/utils.py
+++ b/fastapi/openapi/utils.py
@@ -488,6 +488,7 @@ def get_openapi(
     terms_of_service: Optional[str] = None,
     contact: Optional[Dict[str, Union[str, Any]]] = None,
     license_info: Optional[Dict[str, Union[str, Any]]] = None,
+    prefix: str = "",
     separate_input_output_schemas: bool = True,
 ) -> Dict[str, Any]:
     info: Dict[str, Any] = {"title": title, "version": version}
@@ -529,6 +530,7 @@ def get_openapi(
             )
             if result:
                 path, security_schemes, path_definitions = result
+                route.path_format = f"{prefix}{route.path_format}"
                 if path:
                     paths.setdefault(route.path_format, {}).update(path)
                 if security_schemes:
diff --git a/tests/test_custom_openapi_subapp.py b/tests/test_custom_openapi_subapp.py
new file mode 100644
index 000000000..7b20af864
--- /dev/null
+++ b/tests/test_custom_openapi_subapp.py
@@ -0,0 +1,36 @@
+from fastapi import FastAPI
+from fastapi.openapi.utils import get_openapi
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+sub_app = FastAPI(
+    docs_url=None,
+    redoc_url=None,
+    openapi_url=None,
+)
+
+
+@sub_app.get("/openapi.json")
+async def openapi(
+    # Custom Deps
+):
+    return get_openapi(
+        title="Custom OpenAPI",
+        version="0.1",
+        routes=sub_app.routes,
+        prefix="/sub_app",
+    )
+
+
+app.mount("/sub_app", sub_app)
+
+
+client = TestClient(app)
+
+
+def test_sub_app_open_api():
+    response = client.get("/sub_app/openapi.json")
+    assert response.status_code == 200, response.json()
+    assert response.headers["content-type"] == "application/json"
+    paths = list(response.json()["paths"].keys())
+    assert paths == ["/sub_app/openapi.json"]