With the outbreak of coronavirus disease (COVID-19) caused by novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the world has been facing an unprecedented challenge. Considering the lack of appropriate therapy for COVID-19, it is crucial to develop effective treatments instead of supportive approaches. Mesenchymal stem cells (MSCs) as multipotent stromal cells have been shown to possess treating potency through inhibiting or modulating the pathological events in COVID-19. MSCs and their exosomes participate in immunomodulation by controlling cell-mediated immunity and cytokine release. Furthermore, they repair the renin-angiotensin-aldosterone system (RAAS) malfunction, increase alveolar fluid clearance, and reduce the chance of hypercoagulation. Besides the lung, which is the primary target of SARS-CoV-2, the heart, kidney, nervous system, and gastrointestinal tract are also affected by COVID-19. Thus, the efficacy of targeting these organs via different delivery routes of MSCs and their exosomes should be evaluated to ensure safe and effective MSCs administration in COVID-19. This review focuses on the proposed therapeutic mechanisms and delivery routes of MSCs and their exosomes to the damaged organs. It also discusses the possible application of primed and genetically modified MSCs as a promising drug delivery system in COVID-19. Moreover, the recent advances in the clinical trials of MSCs and MSCs-derived exosomes as one of the promising therapeutic approaches in COVID-19 have been reviewed.