Title: Federated Nearest Neighbor Machine Translation. Abstract: To protect user privacy and meet legal regulations, federated learning (FL) is attracting significant attention. Training neural machine translation (NMT) models with traditional FL algorithm (e.g., FedAvg) typically relies on multi-round model-based interactions. However, it is impractical and inefficient for machine translation tasks due to the vast communication overheads and heavy synchronization. In this paper, we propose a novel federated nearest neighbor (FedNN) machine translation framework that, instead of multi-round model-based interactions, leverages one-round memorization-based interaction to share knowledge across different clients to build low-overhead privacy-preserving systems. The whole approach equips the public NMT model trained on large-scale accessible data with a $k$-nearest-neighbor ($k$NN) classifier and integrates the external datastore constructed by private text data in all clients to form the final FL model.  A two-phase datastore encryption strategy is introduced to achieve privacy-preserving during this process.  Extensive experiments show that FedNN significantly reduces computational and communication costs compared with FedAvg, while maintaining promising performance in different FL settings.