The metaverse integrates physical and virtual realities, enabling humans and their avatars to interact in an environment supported by technologies such as high-speed internet, virtual reality, augmented reality, mixed and extended reality, blockchain, digital twins and artificial intelligence (AI), all enriched by effectively unlimited data. The metaverse recently emerged as social media and entertainment platforms, but extension to healthcare could have a profound impact on clinical practice and human health. As a group of academic, industrial, clinical and regulatory researchers, we identify unique opportunities for metaverse approaches in the healthcare domain. A metaverse of 'medical technology and AI' (MeTAI) can facilitate the development, prototyping, evaluation, regulation, translation and refinement of AI-based medical practice, especially medical imaging-guided diagnosis and therapy. Here, we present metaverse use cases, including virtual comparative scanning, raw data sharing, augmented regulatory science and metaversed medical intervention. We discuss relevant issues on the ecosystem of the MeTAI metaverse including privacy, security and disparity. We also identify specific action items for coordinated efforts to build the MeTAI metaverse for improved healthcare quality, accessibility, cost-effectiveness and patient satisfaction.