A number of medicines are currently under investigation for the treatment of COVID-19 disease including anti-viral, anti-malarial, and anti-inflammatory agents. While these treatments can improve patient's recovery and survival, these therapeutic strategies do not lead to unequivocal restoration of the lung damage inflicted by this disease. Stem cell therapies and, more recently, their secreted extracellular vesicles (EVs), are emerging as new promising treatments, which could attenuate inflammation but also regenerate the lung damage caused by COVID-19. Stem cells exert their immunomodulatory, anti-oxidant, and reparative therapeutic effects likely through their EVs, and therefore, could be beneficial, alone or in combination with other therapeutic agents, in people with COVID-19. In this review article, we outline the mechanisms of cytokine storm and lung damage caused by SARS-CoV-2 virus leading to COVID-19 disease and how mesenchymal stem cells (MSCs) and their secreted EVs can be utilized to tackle this damage by harnessing their regenerative properties, which gives them potential enhanced clinical utility compared to other investigated pharmacological treatments. There are currently 17 clinical trials evaluating the therapeutic potential of MSCs for the treatment of COVID-19, the majority of which are administered intravenously with only one clinical trial testing MSC-derived exosomes via inhalation route. While we wait for the outcomes from these trials to be reported, here we emphasize opportunities and risks associated with these therapies, as well as delineate the major roadblocks to progressing these promising curative therapies toward mainstream treatment for COVID-19.