diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 7c6558c695..40dffba64b 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -826,6 +826,10 @@ def request_params_to_args(
         if value is not None:
             params_to_process[get_validation_alias(field)] = value
         processed_keys.add(alias or get_validation_alias(field))
+        # For headers with convert_underscores=True, mark both the converted
+        # header name and the original field alias as processed to avoid
+        # accepting the original alias as an extra header.
+        processed_keys.add(get_validation_alias(field))
 
     for key in received_params.keys():
         if key not in processed_keys:
diff --git a/tests/test_query_cookie_header_model_extra_params.py b/tests/test_query_cookie_header_model_extra_params.py
index d361e1e533..3fd84dc00e 100644
--- a/tests/test_query_cookie_header_model_extra_params.py
+++ b/tests/test_query_cookie_header_model_extra_params.py
@@ -11,6 +11,10 @@ class Model(BaseModel):
     model_config = {"extra": "allow"}
 
 
+class AuthHeaders(BaseModel):
+    x_user_id: str
+
+
 @app.get("/query")
 async def query_model_with_extra(data: Model = Query()):
     return data
@@ -26,6 +30,11 @@ async def cookies_model_with_extra(data: Model = Cookie()):
     return data
 
 
+@app.get("/header-requires-hyphen")
+async def header_model_requires_hyphen(data: AuthHeaders = Header()):
+    return data
+
+
 def test_query_pass_extra_list():
     client = TestClient(app)
     resp = client.get(
@@ -91,6 +100,32 @@ def test_header_pass_extra_single():
     assert resp_json["param2"] == "456"
 
 
+def test_header_model_prefers_hyphenated_header_with_convert_underscores():
+    client = TestClient(app)
+
+    resp = client.get(
+        "/header-requires-hyphen",
+        headers=[
+            ("x-user-id", "hyphenated-value"),
+            ("x_user_id", "underscore-value"),
+        ],
+    )
+
+    assert resp.status_code == 200
+    assert resp.json() == {"x_user_id": "hyphenated-value"}
+
+
+def test_header_model_rejects_underscore_header_with_convert_underscores():
+    client = TestClient(app)
+
+    resp = client.get(
+        "/header-requires-hyphen", headers={"x_user_id": "underscore-value"}
+    )
+
+    assert resp.status_code == 422
+    assert resp.json()["detail"][0]["loc"] == ["header", "x_user_id"]
+
+
 def test_cookie_pass_extra_list():
     client = TestClient(app)
     client.cookies = [