The Internet of Medical Things (IoMT) is transforming modern healthcare systems by merging technological, economical, and social opportunities and has recently gained traction in the healthcare domain. The severely contagious respiratory syndrome coronavirus called COVID-19 has emerged as a severe threat to public health. COVID-19 is a highly infectious virus that is spread by person-to-person contact. Therefore, minimizing physical interactions between patients and medical healthcare workers is necessary. The significance of technology and its associated potential were fully explored and proven during the outbreak of COVID-19 in all domains of human life. Healthcare systems employ all modes of technology to facilitate the increasing number of COVID-19 patients. The need for remote healthcare was reemphasized, and many remote healthcare solutions were adopted. Various IoMT-based systems were proposed and implemented to support traditional healthcare systems with reaching the maximum number of people remotely. The objective of this research is twofold. First, a systematic literature review (SLR) is conducted to critically evaluate 76 articles on IoMT systems for different medical applications, especially for COVID-19 and other health sectors. Secondly, we briefly review IoMT frameworks and the role of IoMT-based technologies in COVID-19 and propose a framework, named ‘cov-AID’, that remotely monitors and diagnoses the disease. The proposed framework encompasses the benefits of IoMT sensors and extensive data analysis and prediction. Moreover, cov-AID also helps to identify COVID-19 outbreak regions and alerts people not to visit those locations to prevent the spread of infection. The cov-AID is a promising framework for dynamic patient monitoring, patient tracking, quick disease diagnosis, remote treatment, and prevention from spreading the virus to others. We also discuss potential challenges faced in adopting and applying big data technologies to combat COVID-19.