Cancer represents the main cause of morbidity and mortality worldwide, constituting a serious health problem. In this context, melanoma represents the most aggressive and fatal type of skin cancer, with death rates increasing every year. Scientific efforts have been addressed to the development of inhibitors targeting the tyrosinase enzyme as potential anti-melanoma agents due to the importance of this enzyme in melanogenesis biosynthesis. Coumarin-based compounds have shown potential activity as anti-melanoma agents and tyrosinase inhibitors. In this study, coumarin-based derivatives were designed, synthesized, and experimentally evaluated upon tyrosinase. Compound FN-19, a coumarin–thiosemicarbazone analog, exhibited potent anti-tyrosinase activity, with an IC50 value of 42.16 ± 5.16 µM, being more active than ascorbic acid and kojic acid, both reference inhibitors. The kinetic study showed that FN-19 acts as a mixed inhibitor. Still, for this compound, molecular dynamics (MD) simulations were performed to determine the stability of the complex with tyrosinase, generating RMSD, RMSF, and interaction plots. Additionally, docking studies were performed to elucidate the binding pose at the tyrosinase, suggesting that the hydroxyl group of coumarin derivative performs coordinate bonds (bidentate) with the copper(II) ions at distances ranging from 2.09 to 2.61 Å. Then, MM/PBSA calculations revealed that van der Waals interactions are the most relevant intermolecular forces for complex stabilization. Furthermore, it was observed that FN-19 has a binding energy (ΔEMM) value similar to tropolone, a tyrosinase inhibitor. Therefore, the data obtained in this study will be useful for designing and developing novel coumarin-based analogs targeting the tyrosinase enzyme.