The COVID-19 epidemic represents an unprecedented global health emergency, further aggravated by the lack of effective therapies. For this reason, several clinical trials are testing different off-label drugs, already approved for other pathologies. Mesenchymal stem/stromal cells (MSCs) have been tested during the last two decades for the treatment of various pathologic conditions, including acute and chronic lung diseases, both in animal models and in patients. In particular, promising results have been obtained in the experimental therapy of acute respiratory distress syndrome, which represents the most threatening complication of COVID-19 infection. Furthermore, more recently, great interest has been devoted to the possible clinical applications of extracellular vesicles secreted by MSCs, nanoparticles that convey much of the biological effects and of the therapeutic efficacy of their cells of origin. This review summarizes the experimental evidence underlying the possible use of MSCs and of MSC-EVs in severe COVID-19 infection and underlines the need to evaluate the possible efficacy of these therapeutic approaches through controlled studies under the supervision of the Regulatory Authorities.