With the advent of nano-technology, medical sensors and devices are becoming highly miniaturized. Consequently, the number of sensors and medical devices being implanted to accurately monitor and diagnose a disease is increasing. By measuring the symptoms and controlling a medical device as close as possible to the source, these implantable devices are able to save lives. A wireless link between medical sensors and implantable medical devices is essential in the case of closed-loop medical devices, in which symptoms of the diseases are monitored by sensors that are not placed in close proximity of the therapeutic device. Medium Access Control (MAC) is crucial to make it possible for several medical devices to communicate using a shared wireless medium in such a way that minimum delay, maximum throughput, and increased network life-time are guaranteed. To guarantee this Quality of Service (QoS), the MAC protocols control the main sources of limited resource wastage, namely the idle-listening, packet collisions, over-hearing, and packet loss. Traditional MAC protocols designed for body sensor networks are not directly applicable to Implantable Body Sensor Networks (IBSN) because of the dynamic nature of the radio channel within the human body and the strict QoS requirements of IBSN applications. Although numerous MAC protocols are available in the literature, the majority of them are designed for Body Sensor Network (BSN) and Wireless Sensor Network (WSN). To the best of our knowledge, there is so far no research paper that explores the impact of these MAC protocols specifically for IBSN. MAC protocols designed for implantable devices are still in their infancy and one of their most challenging objectives is to be ultra-low-power. One of the technological solutions to achieve this objective so is to integrate the concept of Wake-up radio (WuR) into the MAC design. In this survey, we present a taxonomy of MAC protocols based on their use of WuR technology and identify their bottlenecks to be used in IBSN applications. Furthermore, we present a number of open research challenges and requirements for designing an energy-efficient and reliable wireless communication protocol for IBSN.