Although many anomaly detection approaches have been developed for multivariate time series data, limited effort has been made in federated settings in which multivariate time series data are heterogeneously distributed among different edge devices while data sharing is prohibited. In this paper, we investigate the problem of federated unsupervised anomaly detection and present a Federated Exemplar-based Deep Neural Network (Fed-ExDNN) to conduct anomaly detection for multivariate time series data on different edge devices. Specifically, we first design an Exemplar-based Deep Neural network (ExDNN) for learning local time series representations based on their compatibility with an exemplar module which consists of hidden parameters learned to capture varieties of normal patterns on each edge device. Next, a constrained clustering mechanism (FedCC) is employed on the centralized server to align and aggregate the parameters of different local exemplar modules to obtain a unified global exemplar module. Finally, the global exemplar module is deployed together with a shared feature encoder to each edge device, and anomaly detection is conducted by examining the compatibility of testing data to the exemplar module. Fed-ExDNN captures local normal time series patterns with ExDNN and aggregates these patterns by FedCC, and thus can handle the heterogeneous data distributed over different edge devices simultaneously. Thoroughly empirical studies on six public datasets show that ExDNN and Fed-ExDNN can outperform state-of-the-art anomaly detection algorithms and federated learning techniques, respectively.