Retrieval-based language models (LMs) have demonstrated improved interpretability, factuality, and adaptability compared to their parametric counterparts by incorporating retrieved text from external datastores. While it is well known that parametric models are prone to leaking private data, it remains unclear how the addition of a retrieval datastore impacts model privacy. In this work, we present the first study of privacy risks in retrieval-based LMs, particularly kNN-LMs. Our goal is to explore the optimal design and training procedure in domains where privacy is of concern, aiming to strike a balance between utility and privacy. Crucially, we find that kNN-LMs are more susceptible to leaking private information from their private datastore than parametric models. We further explore mitigations of privacy risks: When privacy information is targeted and readily detected in the text, we find that a simple sanitization step would eliminate the risks while decoupling query and key encoders achieves an even better utility-privacy trade-off. Otherwise, we consider strategies of mixing public and private data in both datastore and encoder training. While these methods offer modest improvements, they leave considerable room for future work. Together, our findings provide insights for practitioners to better understand and mitigate privacy risks in retrieval-based LMs.