Unsupervised image-to-image translation methods such as CycleGAN learn to convert images from one domain to another using unpaired training data sets from different domains. Unfortunately, these approaches still require centrally collected unpaired records, potentially violating privacy and security issues. Although the recent federated learning (FL) allows a neural network to be trained without data exchange, the basic assumption of the FL is that all clients have their own training data from a similar domain, which is different from our image-to-image translation scenario in which each client has images from its unique domain and the goal is to learn image translation between different domains without accessing the target domain data. To address this, here we propose a novel federated CycleGAN architecture that can learn image translation in an unsupervised manner while maintaining the data privacy. Specifically, our approach arises from a novel observation that CycleGAN loss can be decomposed into the sum of client specific local objectives that can be evaluated using only their data. This local objective decomposition allows multiple clients to participate in federated CycleGAN training without sacrificing performance. Furthermore, our method employs novel switchable generator and discriminator architecture using Adaptive Instance Normalization (AdaIN) that significantly reduces the band-width requirement of the federated learning. Our experimental results on various unsupervised image translation tasks show that our federated CycleGAN provides comparable performance compared to the non-federated counterpart.