diff --git a/googleapiclient/discovery.py b/googleapiclient/discovery.py
index a8f59bca5ab..f7bbd77763c 100644
--- a/googleapiclient/discovery.py
+++ b/googleapiclient/discovery.py
@@ -1170,9 +1170,11 @@ def method(self, **kwargs):
         elif "response" not in methodDesc:
             model = RawModel()
 
+        api_version = methodDesc.get("apiVersion", None)
+
         headers = {}
         headers, params, query, body = model.request(
-            headers, actual_path_params, actual_query_params, body_value
+            headers, actual_path_params, actual_query_params, body_value, api_version
         )
 
         expanded_url = uritemplate.expand(pathUrl, params)
diff --git a/googleapiclient/model.py b/googleapiclient/model.py
index 4ba27522357..dee1cb7f377 100644
--- a/googleapiclient/model.py
+++ b/googleapiclient/model.py
@@ -27,10 +27,18 @@
 import logging
 import platform
 import urllib
+import warnings
 
 from googleapiclient import version as googleapiclient_version
 from googleapiclient.errors import HttpError
 
+try:
+    from google.api_core.version_header import API_VERSION_METADATA_KEY
+
+    HAS_API_VERSION = True
+except ImportError:
+    HAS_API_VERSION = False
+
 _LIBRARY_VERSION = googleapiclient_version.__version__
 _PY_VERSION = platform.python_version()
 
@@ -121,7 +129,7 @@ def _log_request(self, headers, path_params, query, body):
             LOGGER.info("query: %s", query)
             LOGGER.info("--request-end--")
 
-    def request(self, headers, path_params, query_params, body_value):
+    def request(self, headers, path_params, query_params, body_value, api_version=None):
         """Updates outgoing requests with a serialized body.
 
         Args:
@@ -129,7 +137,10 @@ def request(self, headers, path_params, query_params, body_value):
           path_params: dict, parameters that appear in the request path
           query_params: dict, parameters that appear in the query
           body_value: object, the request body as a Python object, which must be
-                      serializable by json.
+              serializable by json.
+          api_version: str, The precise API version represented by this request,
+              which will result in an API Version header being sent along with the
+              HTTP request.
         Returns:
           A tuple of (headers, path_params, query, body)
 
@@ -155,6 +166,15 @@ def request(self, headers, path_params, query_params, body_value):
             _PY_VERSION,
         )
 
+        if api_version and HAS_API_VERSION:
+            headers[API_VERSION_METADATA_KEY] = api_version
+        elif api_version:
+            warnings.warn(
+                "The `api_version` argument is ignored as a newer version of "
+                "`google-api-core` is required to use this feature."
+                "Please upgrade `google-api-core` to 2.19.0 or newer."
+            )
+
         if body_value is not None:
             headers["content-type"] = self.content_type
             body_value = self.serialize(body_value)
diff --git a/tests/test_json_model.py b/tests/test_json_model.py
index a34cd6d94b5..1bd75e50850 100644
--- a/tests/test_json_model.py
+++ b/tests/test_json_model.py
@@ -35,6 +35,13 @@
 import googleapiclient.model
 from googleapiclient.model import JsonModel
 
+try:
+    from google.api_core.version_header import API_VERSION_METADATA_KEY
+
+    HAS_API_VERSION = True
+except ImportError:
+    HAS_API_VERSION = False
+
 _LIBRARY_VERSION = googleapiclient_version.__version__
 CSV_TEXT_MOCK = "column1,column2,column3\nstring1,1.2,string2"
 
@@ -172,6 +179,29 @@ def test_x_goog_api_client(self):
             + platform.python_version(),
         )
 
+    @unittest.skipIf(
+        not HAS_API_VERSION,
+        "Skip this test when an older version of google-api-core is used",
+    )
+    def test_x_goog_api_version(self):
+        model = JsonModel(data_wrapper=False)
+
+        # test header composition for clients that wrap discovery
+        headers = {}
+        path_params = {}
+        query_params = {}
+        body = {}
+        api_version = "20240401"
+
+        headers, _, _, body = model.request(
+            headers, path_params, query_params, body, api_version
+        )
+
+        self.assertEqual(
+            headers[API_VERSION_METADATA_KEY],
+            api_version,
+        )
+
     def test_bad_response(self):
         model = JsonModel(data_wrapper=False)
         resp = httplib2.Response({"status": "401"})