Coronavirus disease 2019 (COVID-19) is now at the forefront of major health challenge faced globally, creating an urgent need for safe and efficient therapeutic strategies. Given the high attrition rates, high costs, and quite slow development of drug discovery, repurposing of known FDA-approved molecules is increasingly becoming an attractive issue in order to quickly find molecules capable of preventing and/or curing COVID-19 patients. Cyclosporin A (CsA), a common anti-rejection drug widely used in transplantation, has recently been shown to exhibit substantial anti-SARS-CoV-2 antiviral activity and anti-COVID-19 effect. Here, we review the molecular mechanisms of action of CsA in order to highlight why this molecule seems to be an interesting candidate for the therapeutic management of COVID-19 patients. We conclude that CsA could have at least three major targets in COVID-19 patients: (i) an anti-inflammatory effect reducing the production of proinflammatory cytokines, (ii) an antiviral effect preventing the formation of the viral RNA synthesis complex, and (iii) an effect on tissue damage and thrombosis by acting against the deleterious action of angiotensin II. Several preliminary CsA clinical trials performed on COVID-19 patients report lower incidence of death and suggest that this strategy should be investigated further in order to assess in which context the benefit/risk ratio of repurposing CsA as first-line therapy in COVID-19 is the most favorable.