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The main protease (Mpro) of SARS-CoV-2 is a well-established drug target for rational drug design of COVID-19 inhibitors. To address the serious challenge of COVID-19, we have performed biochemical inhibition screens with recombinantly expressed SARS-CoV-2 main protease (Mpro). A fluorescent assay was used to identify the flavonoid isoquercitrin as an Mpro inhibitor. Both isoquercitrin encapsulated in γ-cyclodextrin (inclusion complex formulations) and alone inhibited SARS-CoV-2 Mpro. For isoquercitrin, a Ki value of 32 μM (IC50 = 63 μM) was obtained. Isoquercitrin γ-cyclodextrin inclusion complex formulations additionally inhibited Zika virus NS2B-NS3pro leading to an IC50 value of 98 μM. Formulations containing the other flavonoid compounds diosmetin-7-O-glucoside, hesperetin-7-O-glucoside, and naringenin-7-O-glucoside did not inhibit SARS-CoV-2 Mpro. Steady-state kinetics indicate that the inhibition mechanism of Mpro by isoquercitrin is potentially competitive. Molecular modeling studies carried out with MM/PBSA confirm the likely modes of isoquercitrin binding to both proteases. These modeling results can be used in the development of structural analogs of isoquercitrin with better inhibitory profiles and potential candidates for anti-coronavirus drugs. Since the targeted proteases are essential for viral activity, the delivery isoquercitrin-cyclodextrin inclusion complex formulations could be of great interest for the development of future antiviral drugs to target intracellular virus proteins or other components.