COVID-19 is a disease caused by severe acute respiratory syndrome coronavirus 2. Presently, there is no effective treatment for COVID-19. As part of the worldwide efforts to find efficient therapies and preventions, it has been reported the crystalline structure of the SARS-CoV-2 main protease M(pro) (also called 3CL(pro)) bound to a synthetic inhibitor, which represents a major druggable target. The druggability of M(pro) could be used for discovering drugs to treat COVID-19. A multilevel computational study was carried out to evaluate the potential antiviral properties of the components of the medicinal herb Uncaria tomentosa (Cat's claw), focusing on the inhibition of M(pro). The in silico approach starts with protein-ligand docking of 26 Cat's claw key components, followed by ligand pathway calculations, molecular dynamics simulations, and MM-GBSA calculation of the free energy of binding for the best docked candidates. The structural bioinformatics approaches led to identification of three bioactive compounds of Uncaria tomentosa (speciophylline, cadambine, and proanthocyanidin B2) with potential therapeutic effects by strong interaction with 3CL(pro). Additionally, in silico drug-likeness indices for these components were calculated and showed good predicted therapeutic profiles of these phytochemicals. Our findings suggest the potential effectiveness of Cat's claw as complementary and/or alternative medicine for COVID-19 treatment.