Instruction-driven image editing allows users to quickly edit an image according to text instructions in a forward pass. Nevertheless, malicious users can easily exploit this technique to create fake images, which could cause a crisis of trust and harm the rights of the original image owners. Watermarking is a common solution to trace such malicious behavior. Unfortunately, instruction-driven image editing can significantly change the watermarked image at the semantic level, making current state-of-the-art watermarking methods ineffective. To remedy it, we propose Robust-Wide, the first robust watermarking methodology against instruction-driven image editing. Specifically, we follow the classic structure of deep robust watermarking, consisting of the encoder, noise layer, and decoder. To achieve robustness against semantic distortions, we introduce a novel Partial Instruction-driven Denoising Sampling Guidance (PIDSG) module, which consists of a large variety of instruction injections and substantial modifications of images at different semantic levels. With PIDSG, the encoder tends to embed the watermark into more robust and semantic-aware areas, which remains in existence even after severe image editing. Experiments demonstrate that Robust-Wide can effectively extract the watermark from the edited image with a low bit error rate of nearly 2.6% for 64-bit watermark messages. Meanwhile, it only induces a neglectable influence on the visual quality and editability of the original images. Moreover, Robust-Wide holds general robustness against different sampling configurations and other popular image editing methods such as ControlNet-InstructPix2Pix, MagicBrush, Inpainting, and DDIM Inversion. Codes and models are available at https://github.com/hurunyi/Robust-Wide.