diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 45e1ff3ed..ef8549b92 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -444,7 +444,9 @@ def analyze_param(
         depends = dataclasses.replace(depends, dependency=type_annotation)
 
     # Handle non-param type annotations like Request
-    if lenient_issubclass(
+    # Only apply special handling when there's no explicit Depends - if there's a Depends,
+    # the dependency will be called and its return value used instead of the special injection
+    if depends is None and lenient_issubclass(
         type_annotation,
         (
             Request,
@@ -455,7 +457,6 @@ def analyze_param(
             SecurityScopes,
         ),
     ):
-        assert depends is None, f"Cannot specify `Depends` for type {type_annotation!r}"
         assert field_info is None, (
             f"Cannot specify FastAPI annotation for type {type_annotation!r}"
         )
diff --git a/tests/test_response_dependency.py b/tests/test_response_dependency.py
new file mode 100644
index 000000000..1c600e484
--- /dev/null
+++ b/tests/test_response_dependency.py
@@ -0,0 +1,89 @@
+"""Test using Response type hint as dependency annotation."""
+
+from typing import Annotated
+
+from fastapi import Depends, FastAPI, Response
+from fastapi.testclient import TestClient
+
+
+def test_response_with_depends_annotated():
+    """Response type hint should work with Annotated[Response, Depends(...)]."""
+    app = FastAPI()
+
+    def modify_response(response: Response) -> Response:
+        response.headers["X-Custom"] = "modified"
+        return response
+
+    @app.get("/")
+    def endpoint(response: Annotated[Response, Depends(modify_response)]):
+        return {"status": "ok"}
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert resp.json() == {"status": "ok"}
+    assert resp.headers.get("X-Custom") == "modified"
+
+
+def test_response_with_depends_default():
+    """Response type hint should work with Response = Depends(...)."""
+    app = FastAPI()
+
+    def modify_response(response: Response) -> Response:
+        response.headers["X-Custom"] = "modified"
+        return response
+
+    @app.get("/")
+    def endpoint(response: Response = Depends(modify_response)):
+        return {"status": "ok"}
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert resp.json() == {"status": "ok"}
+    assert resp.headers.get("X-Custom") == "modified"
+
+
+def test_response_without_depends():
+    """Regular Response injection should still work."""
+    app = FastAPI()
+
+    @app.get("/")
+    def endpoint(response: Response):
+        response.headers["X-Direct"] = "set"
+        return {"status": "ok"}
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert resp.json() == {"status": "ok"}
+    assert resp.headers.get("X-Direct") == "set"
+
+
+def test_response_dependency_chain():
+    """Response dependency should work in a chain of dependencies."""
+    app = FastAPI()
+
+    def first_modifier(response: Response) -> Response:
+        response.headers["X-First"] = "1"
+        return response
+
+    def second_modifier(
+        response: Annotated[Response, Depends(first_modifier)],
+    ) -> Response:
+        response.headers["X-Second"] = "2"
+        return response
+
+    @app.get("/")
+    def endpoint(response: Annotated[Response, Depends(second_modifier)]):
+        return {"status": "ok"}
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert resp.headers.get("X-First") == "1"
+    assert resp.headers.get("X-Second") == "2"