Coxsackievirus A16 (CVA16) is an etiologic agent of hand, foot, and mouth disease (HFMD) that affects young children, and although typically self-limited, severe complications, and fatal cases have been reported. Due to the lack of specific medication and vaccines against CVA16, there is currently a need to develop effective antivirals to better control CVA16 infections in epidemic areas. In this study, we identified the tannins chebulagic acid (CHLA) and punicalagin (PUG) as small molecules that can efficiently disrupt the CVA16 infection of human rhabdomyosarcoma cells. Both compounds significantly reduced CVA16 infectivity at micromolar concentrations without apparent cytotoxicity. A mechanistic analysis revealed that the tannins particularly targeted the CVA16 entry phase by inactivating cell-free viral particles and inhibiting viral binding. Further examination by molecular docking analysis pinpointed the targets of the tannins in the fivefold axis canyon region of the CVA16 capsid near the pocket entrance that functions in cell surface receptor binding. We suggest that CHLA and PUG are efficient antagonists of CVA16 entry and could be of value as antiviral candidates or as starting points for developing molecules to treat CVA16 infections.