The potential outcome of flavivirus and alphavirus co-infections is worrisome due to the development of severe diseases. Hundreds of millions of people worldwide live under the risk of infections caused by viruses like chikungunya virus (CHIKV, genus Alphavirus), dengue virus (DENV, genus Flavivirus), and zika virus (ZIKV, genus Flavivirus). So far, neither any drug exists against the infection by a single virus, nor against co-infection. The results described in our study demonstrate the inhibitory potential of two flavonoids derived from citrus plants: Hesperetin (HST) against NS2B/NS3^pro of ZIKV and nsP2^pro of CHIKV and, Hesperidin (HSD) against nsP2^pro of CHIKV. The flavonoids are noncompetitive inhibitors and the determined IC₅₀ values are in low µM range for HST against ZIKV NS2B/NS3^pro (12.6 ± 1.3 µM) and against CHIKV nsP2^pro (2.5 ± 0.4 µM). The IC₅₀ for HSD against CHIKV nsP2^pro was 7.1 ± 1.1 µM. The calculated ligand efficiencies for HST were > 0.3, which reflect its potential to be used as a lead compound. Docking and molecular dynamics simulations display the effect of HST and HSD on the protease 3D models of CHIKV and ZIKV. Conformational changes after ligand binding and their effect on the substrate-binding pocket of the proteases were investigated. Additionally, MTT assays demonstrated a very low cytotoxicity of both the molecules. Based on our results, we assume that HST comprise a chemical structure that serves as a starting point molecule to develop a potent inhibitor to combat CHIKV and ZIKV co-infections by inhibiting the virus proteases.