We establish a connection between federated learning, a concept from machine learning, and mean-field games, a concept from game theory and control theory. In this analogy, the local federated learners are considered as the players and the aggregation of the gradients in a central server is the mean-field effect. We present federated learning as a differential game and discuss the properties of the equilibrium of this game. We hope this novel view to federated learning brings together researchers from these two distinct areas to work on fundamental problems of large-scale distributed and privacy-preserving learning algorithms.