Zero-shot inference is a powerful paradigm that enables the use of large pretrained models for downstream classification tasks without further training. However, these models are vulnerable to inherited biases that can impact their performance. The traditional solution is fine-tuning, but this undermines the key advantage of pretrained models, which is their ability to be used out-of-the-box. We propose RoboShot, a method that improves the robustness of pretrained model embeddings in a fully zero-shot fashion. First, we use language models (LMs) to obtain useful insights from task descriptions. These insights are embedded and used to remove harmful and boost useful components in embeddings---without any supervision. Theoretically, we provide a simple and tractable model for biases in zero-shot embeddings and give a result characterizing under what conditions our approach can boost performance. Empirically, we evaluate RoboShot on nine image and NLP classification tasks and show an average improvement of 15.98% over several zero-shot baselines. Additionally, we demonstrate that RoboShot is compatible with a variety of pretrained and language models and propose a way to further boost performance with a zero-shot adaptation variant.