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Domain adaptation has been vastly investigated in computer vision but still requires access to target images at train time, which might be intractable in some uncommon conditions. In this paper, we propose the task of `Prompt-driven Zero-shot Domain Adaptation', where we adapt a model trained on a source domain using only a general description in natural language of the target domain, i.e., a prompt. First, we leverage a pretrained contrastive vision-language model (CLIP) to optimize affine transformations of source features, steering them towards the target text embedding while preserving their content and semantics. To achieve this, we propose Prompt-driven Instance Normalization (PIN). Second, we show that these prompt-driven augmentations can be used to perform zero-shot domain adaptation for semantic segmentation. Experiments demonstrate that our method significantly outperforms CLIP-based style transfer baselines on several datasets for the downstream task at hand, even surpassing one-shot unsupervised domain adaptation. A similar boost is observed on object detection and image classification. The code is available at https://github.com/astra-vision/PODA .