Despite the significant benefits that the rise of Internet of Medical Things (IoMT) can bring into citizens’ quality of life by enabling IoMT-based healthcare monitoring systems, there is an urgent need for novel security mechanisms to address the pressing security challenges of IoMT edge networks in an effective and efficient manner before they gain the trust of all involved stakeholders and reach their full potential in the market of next generation IoMT-based healthcare monitoring systems. In this context, blockchain technology has been foreseen by the industry and research community as a disruptive technology that can be integrated into novel security solutions for IoMT edge networks, as it can play a significant role in securing IoMT devices and resisting unauthorized access during data transmission (i.e., tamper-proof transmission of medical data). However, despite the fact that several blockchain-based security mechanisms have already been proposed in the literature for different types of IoT edge networks, there is a lack of blockchain-based security mechanisms for IoMT edge networks, and thus more effort is required to be put on the design and development of security mechanisms relying on blockchain technology for such networks. Towards this direction, the first step is the comprehensive understanding of the following two types of blockchain-based security mechanisms: (a) the very few existing ones specifically designed for IoMT edge networks, and (b) those designed for other types of IoT networks but could be possibly adopted in IoMT edge networks due to similar capabilities and technical characteristics. Therefore, in this paper, we review the state-of-the-art of the above two types of blockchain-based security mechanisms in order to provide a foundation for organizing research efforts towards the design and development of reliable blockchain-based countermeasures, addressing the pressing security challenges of IoMT edge networks in an effective and efficient manner.