Federated learning methods enable model training across distributed data sources without data leaving their original locations and have gained increasing interest in various fields. However, existing approaches are limited, excluding many structured probabilistic models. We present a general and elegant solution based on structured variational inference, widely used in Bayesian machine learning, adapted for the federated setting. Additionally, we provide a communication-efficient variant analogous to the canonical FedAvg algorithm. The proposed algorithms' effectiveness is demonstrated, and their performance is compared with hierarchical Bayesian neural networks and topic models.