Arthropod-borne viruses within the Flaviviridae family such as Zika (ZIKV) and dengue (DENV) are responsible for major outbreaks in tropical countries, and there are no specific treatments against them. Naringenin and 7-O-methyl naringenin are flavonoids that can be extracted from geopropolis, a natural material that the Brazilian Jandaira stingless bee (Melipona subnitida Ducke) produces to protect its nest. Here, these flavonoids were tested against ZIKV and DENV using Vero cells as a cellular model to perform a cytotoxicity assay and to define the effective concentrations of TCID50 as the readout method. The results demonstrated the antiviral activity of the compounds against both viruses upon the treatment of infected cells. The tested flavonoids had antiviral activity comparable with 6-methylmercaptopurine riboside (6-MMPr), used here as a positive control. In addition, to identify the possible action mechanism of the antiviral candidates, we carried out a docking analysis followed by a molecular dynamics simulation to elucidate naringenin and 7-O-methyl naringenin binding sites to each virus. Altogether, these results demonstrate that both flavonoids have potent antiviral effects against both viruses and warrant further in vivo trials.