diff --git a/fastapi/routing.py b/fastapi/routing.py
index 36acb6b89d..8fc7e3a465 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -890,6 +890,8 @@ class APIRoute(routing.Route):
         if methods is None:
             methods = ["GET"]
         self.methods: set[str] = {method.upper() for method in methods}
+        if "GET" in self.methods:
+            self.methods.add("HEAD")
         if isinstance(generate_unique_id_function, DefaultPlaceholder):
             current_generate_unique_id: Callable[[APIRoute], str] = (
                 generate_unique_id_function.value
diff --git a/tests/test_auto_head.py b/tests/test_auto_head.py
new file mode 100644
index 0000000000..485a6e8bc4
--- /dev/null
+++ b/tests/test_auto_head.py
@@ -0,0 +1,57 @@
+"""Test that HEAD requests are automatically supported for GET routes (issue #1773)."""
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+
+
+def test_head_for_get_route():
+    """HEAD request on a GET route should return 200, not 405."""
+    app = FastAPI()
+
+    @app.get("/")
+    def read_root():
+        return {"Hello": "World"}
+
+    client = TestClient(app)
+    response = client.head("/")
+    assert response.status_code == 200
+    assert response.headers.get("content-type") is not None
+
+
+def test_head_for_get_route_with_path():
+    """HEAD request on a parameterized GET route should work."""
+    app = FastAPI()
+
+    @app.get("/items/{item_id}")
+    def read_item(item_id: int):
+        return {"item_id": item_id}
+
+    client = TestClient(app)
+    response = client.head("/items/42")
+    assert response.status_code == 200
+
+
+def test_head_not_auto_added_for_post():
+    """POST routes should NOT automatically support HEAD."""
+    app = FastAPI()
+
+    @app.post("/items/")
+    def create_item():
+        return {"created": True}
+
+    client = TestClient(app)
+    response = client.head("/items/")
+    assert response.status_code == 405
+
+
+def test_head_response_has_no_body():
+    """HEAD response should have no body content."""
+    app = FastAPI()
+
+    @app.get("/")
+    def read_root():
+        return {"Hello": "World"}
+
+    client = TestClient(app)
+    response = client.head("/")
+    assert response.status_code == 200
+    assert response.content == b""