Coronavirus disease 2019 (COVID-19), the pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which counts more than 650 million cases and more than 6.6 million of deaths worldwide, affects the respiratory system with typical symptoms such as fever, cough, sore throat, acute respiratory distress syndrome (ARDS), and fatigue. Other nonpulmonary manifestations are related with abnormal inflammatory response, the “cytokine storm”, that could lead to a multiorgan disease and to death. Evolution of effective vaccines against SARS-CoV-2 provided multiple options to prevent the infection, but the treatment of the severe forms remains difficult to manage. The cytokine storm is usually counteracted with standard medical care and anti-inflammatory drugs, but researchers moved forward their studies on new strategies based on cell therapy approaches. The perinatal tissues, such as placental membranes, amniotic fluid, and umbilical cord derivatives, are enriched in mesenchymal stromal cells (MSCs) that exert a well-known anti-inflammatory role, immune response modulation, and tissue repair. In this review, we focused on umbilical-cord-derived MSCs (UC-MSCs) used in in vitro and in vivo studies in order to evaluate the weakening of the severe symptoms, and on recent clinical trials from different databases, supporting the favorable potential of UC-MSCs as therapeutic strategy.