The Internet of Medical Things (IoMT) couples IoT technologies with healthcare services in order to support real-time, remote patient monitoring and treatment. However, the interconnectivity of critical medical devices with other systems in various network layers creates new opportunities for remote adversaries. Since most of the communication protocols have not been specifically designed for the needs of connected medical devices, there is a need to classify the available IoT communication technologies in terms of security. In this paper we classify IoT communication protocols, with respect to their application in IoMT. Then we describe the main characteristics of IoT communication protocols used at the perception, network and application layer of medical devices. We examine the inherent security characteristics and limitations of IoMT-specific communication protocols. Based on realistic attacks we identify available mitigation controls that may be applied to secure IoMT communications, as well as existing research and implementation gaps.