Telemedicine over Internet of Things (IoT) generates an unprecedented amount of data, which further requires transmission, analysis, and storage. Deploying cloud computing to handle data of this magnitude will introduce unacceptable data analysis latency and high storage costs. Thus, mobile edge computing (MEC) deployed between the cloud and users, which is close to the nodes of data generation, can tackle these problems in 5G scenarios with the help of artificial intelligence. This paper proposes a telemedicine system based on MEC and artificial intelligence for remote health monitoring and automatic disease diagnosis. The integration of different technologies such as computers, medicine, and telecommunications will significantly improve the efficiency of patient treatment and reduce the cost of health care.