Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral proteins interact with the eukaryotic translation machinery, and inhibitors of translation have potent antiviral effects. We found that the drug plitidepsin (aplidin), which has limited clinical approval, possesses antiviral activity (90% inhibitory concentration = 0.88 nM) that is more potent than remdesivir against SARS-CoV-2 in vitro by a factor of 27.5, with limited toxicity in cell culture. Through the use of a drug-resistant mutant, we show that the antiviral activity of plitidepsin against SARS-CoV-2 is mediated through inhibition of the known target eEF1A (eukaryotic translation elongation factor 1A). We demonstrate the in vivo efficacy of plitidepsin treatment in two mouse models of SARS-CoV-2 infection with a reduction of viral replication in the lungs by two orders of magnitude using prophylactic treatment. Our results indicate that plitidepsin is a promising therapeutic candidate for COVID-19.