We have witnessed an unprecedented public health crisis caused by the new coronavirus disease (COVID-19), which has severely affected medical institutions, our common lives, and social-economic activities. This crisis also reveals the brittleness of existing medical services, such as over-centralization of medical resources, the hysteresis of medical services digitalization, and weak security and privacy protection of medical data. The integration of the Internet of Medical Things (IoMT) and blockchain is expected to be a panacea to COVID-19 attributed to the ubiquitous presence and the perception of IoMT as well as the enhanced security and immutability of the blockchain. However, the synergy of IoMT and blockchain is also faced with challenges in privacy, latency, and context-absence. The emerging edge intelligence technologies bring opportunities to tackle these issues. In this article, we present a blockchain-empowered edge intelligence for IoMT in addressing the COVID-19 crisis. We first review IoMT, edge intelligence, and blockchain in addressing the COVID-19 pandemic. We then present an architecture of blockchain-empowered edge intelligence for IoMT after discussing the opportunities of integrating blockchain and edge intelligence. We next offer solutions to COVID-19 brought by blockchain-empowered edge intelligence from 1) monitoring and tracing COVID-19 pandemic origin, 2) traceable supply chain of injectable medicines and COVID-19 vaccines, and 3) telemedicine and remote healthcare services. Moreover, we also discuss the challenges and open issues in blockchain-empowered edge intelligence.