The advancement of Internet of Things technologies is enabling continuous monitoring of patients at home and in hospitals. However, Internet of Things architectures still face many challenges regarding power efficiency and scalability at a low cost in order to realize massive ubiquitous deployment, especially in clinical environments. In this paper the benefits of combining data and power into a single cable that the Power over Ethernet standard provides have been leveraged by designing a Power over Ethernet enabled Internet of Things gateway which delivers both cloud connectivity and energy to medical sensors and smart hospital appliances. In addition, the gateway has been customized for processing and transmission of health related data in order to alleviate the processing overhead that wireless sensors have allowing them to extend the battery lifetime and overall system energy efficiency and performance.