Medical robots can play an important role in mitigating the spread of infectious diseases and delivering quality care to patients during the COVID-19 pandemic. Methods and procedures involving medical robots in the continuum of care, ranging from disease prevention, screening, diagnosis, treatment, and homecare have been extensively deployed and also present incredible opportunities for future development. This paper provides an overview of the current state-of-the-art, highlighting the enabling technologies and unmet needs for prospective technological advances within the next 5-10 years. We also identify key research and knowledge barriers that need to be addressed in developing effective and flexible solutions to ensure preparedness for rapid and scalable deployment to combat infectious diseases.