diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index 09e5048cc..e4c32c03e 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -356,6 +356,8 @@ async def _handle_post_request(self, ctx: RequestContext) -> None:
                             error_data = ErrorData(code=METHOD_NOT_FOUND, message="Not Found")
                         else:
                             error_data = ErrorData(code=INVALID_REQUEST, message="Session terminated")
+                    elif response.status_code == 401:
+                        error_data = ErrorData(code=INTERNAL_ERROR, message="Unauthorized")
                     else:
                         error_data = ErrorData(code=INTERNAL_ERROR, message="Server returned an error response")
                     session_message = SessionMessage(JSONRPCError(jsonrpc="2.0", id=message.id, error=error_data))
diff --git a/tests/client/test_streamable_http.py b/tests/client/test_streamable_http.py
index defda41f8..8e76caaf5 100644
--- a/tests/client/test_streamable_http.py
+++ b/tests/client/test_streamable_http.py
@@ -18,6 +18,7 @@
 from mcp_types import (
     CLIENT_CAPABILITIES_META_KEY,
     CLIENT_INFO_META_KEY,
+    INTERNAL_ERROR,
     METHOD_NOT_FOUND,
     PROTOCOL_VERSION_META_KEY,
     JSONRPCError,
@@ -124,6 +125,32 @@ def handler(request: httpx.Request) -> httpx.Response:
     assert reply.message.error.code == METHOD_NOT_FOUND
 
 
+@pytest.mark.anyio
+async def test_bare_401_request_maps_to_unauthorized_jsonrpc_error() -> None:
+    """A bare HTTP 401 should reach the caller as a correlated JSON-RPC error.
+
+    Authorization failures can be operation-specific. The client transport must
+    leave room for the agent/session layer to handle the denial instead of
+    collapsing it into an indistinguishable transport failure.
+    """
+
+    def handler(request: httpx.Request) -> httpx.Response:
+        return httpx.Response(401)
+
+    with anyio.fail_after(5):
+        async with (
+            httpx.AsyncClient(transport=httpx.MockTransport(handler)) as http,
+            streamable_http_client("http://test/mcp", http_client=http) as (read, write),
+        ):
+            await write.send(SessionMessage(JSONRPCRequest(jsonrpc="2.0", id=1, method="tools/call", params={})))
+            reply = await read.receive()
+    assert isinstance(reply, SessionMessage)
+    assert isinstance(reply.message, JSONRPCError)
+    assert reply.message.id == 1
+    assert reply.message.error.code == INTERNAL_ERROR
+    assert reply.message.error.message == "Unauthorized"
+
+
 @pytest.mark.anyio
 async def test_initialize_post_clears_cached_pv_header_and_unstamped_posts_read_it() -> None:
     """``initialize`` discards the cached protocol-version header; every other POST reads it.