Metal-based drugs represent a rich source of chemical substances of potential interest for the treatment of COVID-19. To this end, we have developed a small but representative panel of nine metal compounds, including both synthesized and commercially available complexes, suitable for medical application and tested them in vitro against the SARS-CoV-2 virus. The screening revealed that three compounds from the panel, i.e., the organogold(III) compound Aubipyc, the ruthenium(III) complex KP1019, and antimony trichloride (SbCl3), are endowed with notable antiviral properties and an acceptable cytotoxicity profile. These initial findings prompted us to perform a computational study to unveil the likely molecular basis of their antiviral actions. Calculations evidenced that the metalation of nucleophile sites in SARS-CoV-2 proteins or nucleobase strands, induced by Aubipyc, SbCl3, and KP1019, is likely to occur. Remarkably, we found that only the deprotonated forms of Cys and Sec residues can react favorably with these metallodrugs. The mechanistic implications of these findings are discussed.