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Data privacy is a central problem for embodied agents that can perceive the environment, communicate with humans, and act in the real world. While helping humans complete tasks, the agent may observe and process sensitive information of users, such as house environments, human activities, etc. In this work, we introduce privacy-preserving embodied agent learning for the task of Vision-and-Language Navigation (VLN), where an embodied agent navigates house environments by following natural language instructions. We view each house environment as a local client, which shares nothing other than local updates with the cloud server and other clients, and propose a novel federated vision-and-language navigation (FedVLN) framework to protect data privacy during both training and pre-exploration. Particularly, we propose a decentralized training strategy to limit the data of each client to its local model training and a federated pre-exploration method to do partial model aggregation to improve model generalizability to unseen environments. Extensive results on R2R and RxR datasets show that under our FedVLN framework, decentralized VLN models achieve comparable results with centralized training while protecting seen environment privacy, and federated pre-exploration significantly outperforms centralized pre-exploration while preserving unseen environment privacy.