Cross-domain recommendation (CDR) aims to improve recommendation accuracy in sparse domains by transferring knowledge from data-rich domains. However, existing CDR methods often assume the availability of user-item interaction data across domains, overlooking user privacy concerns. Furthermore, these methods suffer from performance degradation in scenarios with sparse overlapping users, as they typically depend on a large number of fully shared users for effective knowledge transfer. To address these challenges, we propose a Federated Prototype-based Contrastive Learning (CL) method for Privacy-Preserving CDR, named FedPCL-CDR. This approach utilizes non-overlapping user information and prototypes to improve multi-domain performance while protecting user privacy. FedPCL-CDR comprises two modules: local domain (client) learning and global server aggregation. In the local domain, FedPCL-CDR clusters all user data to learn representative prototypes, effectively utilizing non-overlapping user information and addressing the sparse overlapping user issue. It then facilitates knowledge transfer by employing both local and global prototypes returned from the server in a CL manner. Simultaneously, the global server aggregates representative prototypes from local domains to learn both local and global prototypes. The combination of prototypes and federated learning (FL) ensures that sensitive user data remains decentralized, with only prototypes being shared across domains, thereby protecting user privacy. Extensive experiments on four CDR tasks using two real-world datasets demonstrate that FedPCL-CDR outperforms the state-of-the-art baselines.