The autonomic Internet of Things is the creation of self-management capability in the Internet of Things system by embedding some autonomic properties, with the goal of freeing humans from all detail of the operation and management of the system. At same time, this provides a system to always operate on the best performance. This paper presents a review of the recent studies related to the design of network communication protocol, which can support autonomic Internet of Things. Many of the studies come from the research and development in Wireless Sensor Network protocols, as it becomes one of the key technologies for the Internet of Things. The identified autonomic properties are self-organization, self-optimization, and self-protection. We review some protocols with the objective of energy consumption reduction and energy harvesting awareness, as it can support the self-energy-awareness property. As the result, the protocol designs are mapped according to each autonomic property supported, including protocols for MAC layer, protocols for clustering, protocols for routing, and protocols for security. This can be used to map the advances of communication protocol research for the autonomic Internet of Things and to identify the opportunities for future research.