We introduce a rehearsal-free federated domain incremental learning framework, RefFiL, based on a global prompt-sharing paradigm to alleviate catastrophic forgetting challenges in federated domain-incremental learning, where unseen domains are continually learned. Typical methods for mitigating forgetting, such as the use of additional datasets and the retention of private data from earlier tasks, are not viable in federated learning (FL) due to devices' limited resources. Our method, RefFiL, addresses this by learning domain-invariant knowledge and incorporating various domain-specific prompts from the domains represented by different FL participants. A key feature of RefFiL is the generation of local fine-grained prompts by our domain adaptive prompt generator, which effectively learns from local domain knowledge while maintaining distinctive boundaries on a global scale. We also introduce a domain-specific prompt contrastive learning loss that differentiates between locally generated prompts and those from other domains, enhancing RefFiL's precision and effectiveness. Compared to existing methods, RefFiL significantly alleviates catastrophic forgetting without requiring extra memory space, making it ideal for privacy-sensitive and resource-constrained devices.