diff --git a/src/mcp/client/stdio/__init__.py b/src/mcp/client/stdio/__init__.py
index 0d76bb958..8d772a7a6 100644
--- a/src/mcp/client/stdio/__init__.py
+++ b/src/mcp/client/stdio/__init__.py
@@ -155,12 +155,22 @@ async def stdout_reader():
                             message = types.JSONRPCMessage.model_validate_json(line)
                         except Exception as exc:  # pragma: no cover
                             logger.exception("Failed to parse JSONRPC message from server")
-                            await read_stream_writer.send(exc)
+                            try:
+                                await read_stream_writer.send(exc)
+                            except (anyio.ClosedResourceError, anyio.BrokenResourceError):
+                                # Context is closing; exit gracefully (issue #1960).
+                                return
                             continue
 
                         session_message = SessionMessage(message)
-                        await read_stream_writer.send(session_message)
-        except anyio.ClosedResourceError:  # pragma: no cover
+                        try:
+                            await read_stream_writer.send(session_message)
+                        except (anyio.ClosedResourceError, anyio.BrokenResourceError):
+                            # Context is closing; exit gracefully (issue #1960).
+                            # Happens when the caller exits the stdio_client context
+                            # while the subprocess is still writing to stdout.
+                            return
+        except (anyio.ClosedResourceError, anyio.BrokenResourceError):  # pragma: no cover
             await anyio.lowlevel.checkpoint()
 
     async def stdin_writer():
diff --git a/tests/client/test_stdio.py b/tests/client/test_stdio.py
index ba58da732..21fcb13d2 100644
--- a/tests/client/test_stdio.py
+++ b/tests/client/test_stdio.py
@@ -33,6 +33,45 @@ async def test_stdio_context_manager_exiting():
         pass
 
 
+@pytest.mark.anyio
+async def test_stdio_client_exits_cleanly_while_server_still_writing():
+    """Regression test for #1960.
+
+    Exiting the ``stdio_client`` context while the subprocess is still writing to
+    stdout used to surface ``anyio.BrokenResourceError`` through the task group
+    (as an ``ExceptionGroup``). The ``finally`` block closes
+    ``read_stream_writer`` while the background ``stdout_reader`` task is
+    mid-``send``.
+
+    The fix makes ``stdout_reader`` catch both ``ClosedResourceError`` and
+    ``BrokenResourceError`` and return cleanly, so exiting the context is a
+    no-op no matter what the subprocess is doing.
+    """
+    # A server that emits a large burst of valid JSON-RPC notifications without
+    # ever reading stdin. When we exit the context below, the subprocess is
+    # still in the middle of that burst, which is the exact shape of the race.
+    noisy_script = textwrap.dedent(
+        """
+        import sys
+        for i in range(1000):
+            sys.stdout.write(
+                '{"jsonrpc":"2.0","method":"notifications/message",'
+                '"params":{"level":"info","data":"line ' + str(i) + '"}}\\n'
+            )
+            sys.stdout.flush()
+        """
+    )
+
+    server_params = StdioServerParameters(command=sys.executable, args=["-c", noisy_script])
+
+    # The ``async with`` must complete without an ``ExceptionGroup`` /
+    # ``BrokenResourceError`` propagating. ``anyio.fail_after`` prevents a
+    # regression from hanging CI.
+    with anyio.fail_after(5.0):
+        async with stdio_client(server_params) as (_, _):
+            pass
+
+
 @pytest.mark.anyio
 @pytest.mark.skipif(tee is None, reason="could not find tee command")
 async def test_stdio_client():