The outbreak of the COVID-19 pandemic has deeply influenced the lifestyle of the general public and the healthcare system of the society. As a promising approach to address the emerging challenges caused by the epidemic of infectious diseases like COVID-19, Internet of Medical Things (IoMT) deployed in hospitals, clinics, and healthcare centers can save the diagnosis time and improve the efficiency of medical resources though privacy and security concerns of IoMT stall the wide adoption. In order to tackle the privacy, security, and interoperability issues of IoMT, we propose a framework of blockchain-enabled IoMT by introducing blockchain to incumbent IoMT systems. In this paper, we review the benefits of this architecture and illustrate the opportunities brought by blockchain-enabled IoMT. We also provide use cases of blockchain-enabled IoMT on fighting against the COVID-19 pandemic, including the prevention of infectious diseases, location sharing and contact tracing, and the supply chain of injectable medicines. We also outline future work in this area.