Machine Learning, and in particular Federated Machine Learning, opens new perspectives in terms of medical research and patient care. Although Federated Machine Learning improves over centralized Machine Learning in terms of privacy, it does not provide provable privacy guarantees. Furthermore, Federated Machine Learning is quite expensive in term of bandwidth consumption as it requires participant nodes to regularly exchange large updates. This paper proposes a bandwidth-efficient privacy-preserving Federated Learning that provides theoretical privacy guarantees based on Differential Privacy. We experimentally evaluate our proposal for in-hospital mortality prediction using a real dataset, containing Electronic Health Records of about one million patients. Our results suggest that strong and provable patient-level privacy can be enforced at the expense of only a moderate loss of prediction accuracy.