The COVID-19 pandemic has revealed several limitations of existing healthcare systems. Thus, there is a surge in healthcare innovation and new business models using computer-mediated virtual environments to provide an alternative healthcare system. Today, digital transformation is not limited to virtual communication alone but encompasses digitalizing the network of social connections in the healthcare industry using metaverse technology. The metaverse is a universal and immersive virtual world facilitated by virtual reality (VR) and augmented reality (AR). This paper presents the first effort to offer a comprehensive survey that examines the latest metaverse developments in the healthcare industry, which covers seven domains: telemedicine, clinical care, education, mental health, physical fitness, veterinary, and pharmaceuticals. We review metaverse applications and deeply discuss technical issues and available solutions in each domain that can help develop a self-sustaining, persistent, and future-proof solution for medical healthcare systems. Finally, we highlight the challenges that must be tackled before fully embracing the metaverse for the healthcare industry.