diff --git a/src/mcp/server/lowlevel/server.py b/src/mcp/server/lowlevel/server.py
index aee644040..0ba7b2c0f 100644
--- a/src/mcp/server/lowlevel/server.py
+++ b/src/mcp/server/lowlevel/server.py
@@ -417,11 +417,14 @@ async def _handle_message(
                         )
                 case Exception():
                     logger.error(f"Received exception from stream: {message}")
-                    await session.send_log_message(
-                        level="error",
-                        data="Internal Server Error",
-                        logger="mcp.server.exception_handler",
-                    )
+                    try:
+                        await session.send_log_message(
+                            level="error",
+                            data="Internal Server Error",
+                            logger="mcp.server.exception_handler",
+                        )
+                    except (anyio.ClosedResourceError, anyio.BrokenResourceError):
+                        logger.debug("Could not send error log to client: connection already closed")
                     if raise_exceptions:
                         raise message
                 case _:
diff --git a/tests/server/test_lowlevel_exception_handling.py b/tests/server/test_lowlevel_exception_handling.py
index 848b35b29..f2fd51c10 100644
--- a/tests/server/test_lowlevel_exception_handling.py
+++ b/tests/server/test_lowlevel_exception_handling.py
@@ -72,3 +72,52 @@ async def test_normal_message_handling_not_affected():
 
     # Verify _handle_request was called
     server._handle_request.assert_called_once()
+
+
+@pytest.mark.anyio
+@pytest.mark.parametrize(
+    "error_class",
+    [
+        pytest.param("ClosedResourceError", id="closed"),
+        pytest.param("BrokenResourceError", id="broken"),
+    ],
+)
+async def test_exception_handling_tolerates_closed_write_stream(error_class: str):
+    """send_log_message failure on a disconnected client should not crash the server.
+
+    Regression test for https://github.com/modelcontextprotocol/python-sdk/issues/2064.
+    When a client disconnects during request handling, the error handler tries to
+    send a log message back. If the write stream is already closed, the resulting
+    ClosedResourceError/BrokenResourceError should be caught silently.
+    """
+    import anyio
+
+    server = Server("test-server")
+    session = Mock(spec=ServerSession)
+
+    exc_cls = getattr(anyio, error_class)
+    session.send_log_message = AsyncMock(side_effect=exc_cls())
+
+    test_exception = RuntimeError("Client disconnected")
+
+    # Should NOT raise — the ClosedResourceError from send_log_message is caught
+    await server._handle_message(test_exception, session, {}, raise_exceptions=False)
+
+    # send_log_message was still attempted
+    session.send_log_message.assert_called_once()
+
+
+@pytest.mark.anyio
+async def test_exception_handling_reraises_with_closed_stream():
+    """When raise_exceptions=True AND the write stream is closed, the original
+    exception should still be re-raised (not the ClosedResourceError)."""
+    import anyio
+
+    server = Server("test-server")
+    session = Mock(spec=ServerSession)
+    session.send_log_message = AsyncMock(side_effect=anyio.ClosedResourceError())
+
+    test_exception = RuntimeError("Original error")
+
+    with pytest.raises(RuntimeError, match="Original error"):
+        await server._handle_message(test_exception, session, {}, raise_exceptions=True)