DNN-based face recognition models require large centrally aggregated face datasets for training. However, due to the growing data privacy concerns and legal restrictions, accessing and sharing face datasets has become exceedingly difficult. We propose FedFace, a federated learning (FL) framework for collaborative learning of face recognition models in a privacy preserving manner. FedFace utilizes the face images available on multiple clients to learn an accurate and generalizable face recognition model where the face images stored at each client are neither shared with other clients nor the central host. We tackle the a challenging and yet realistic scenario where each client is a mobile device containing face images pertaining to only the owner of the device (one identity per client). Conventional FL algorithms such as FedAvg are not suitable for this setting because they lead to a trivial solution where all the face features collapse into a single point in the embedding space. Our experiments show that FedFace can utilize face images available on 1,000 mobile devices to enhance the performance of a pre-trained face recognition model, CosFace, from a TAR of 81.43% to 83.79% on IJB-A (@ 0.1% FAR). For LFW, the recognition accuracy under the LFW protocol is increased from 99.15% to 99.28%. FedFace is able to do this while ensuring that the face images are never shared between devices or between the device and the server. Our code and pre-trained models will be publicly available.