Internet of Things (IoT) is making strong advances in healthcare with the promise of transformation in technological, social and economic prospects, paving the way for a healthy future. Medical devices equipped with wireless communication enable remote monitoring features and are increasingly becoming connected to each other and to the Internet. Such smart and connected medical devices referred to as the Internet of Medical Things have enabled continuous real-time patient monitoring, increase in diagnostic accuracy, and effective treatment. In spite of their numerous benefits, these devices open up newer attack surfaces thereby introducing multitude of security and privacy concerns. Attacks on Internet connected medical devices can potentially cause significant physical harm and life-threatening damage to the patients. In this research, we design and develop a novel mobile agent based intrusion detection system to secure the network of connected medical devices. In particular, the proposed system is hierarchical, autonomous, and employs machine learning and regression algorithms to detect network level intrusions as well as anomalies in sensor data. We simulate a hospital network topology and perform detailed experiments for various subsets of Internet of Medical things including wireless body area networks and other connected medical devices. Our simulation results demonstrate that we are able to achieve high detection accuracy with minimal resource overhead.