Polyphenols synthesized by plants and fungi have various pharmacological effects. The ability of polyphenols to modulate sirtuins has gained considerable interest due to the role of sirtuins in aging, insulin sensitivity, lipid metabolism, inflammation, and cancer. In particular, sirtuin 6 (SIRT6) has gained importance in regulating a variety of cellular processes, including genomic stability and glucose metabolism. On the other hand, quercetin has been demonstrated to modulate sirtuins and to protect against several chronic diseases. In this study, two quercetin derivatives, diquercetin and 2-chloro-1,4-naphtoquinone-quercetin, were identified as promising SIRT6 inhibitors with IC50 values of 130 μM and 55 μM, respectively. 2-Chloro-1,4-naphtoquinone-quercetin also showed potent inhibition against SIRT2, with an IC50 value of 14 μM. Diquercetin increased the Km value of NAD+, whereas 2-chloro-1,4-naphthoquinone-quercetin increased the Km value of the acetylated substrate. Molecular docking studies suggest that diquercetin prefers the binding site of the nicotinamide (NAM) moiety, whereas 2-chloro-1,4-naphtoquinone-quercetin prefers to dock into the substrate binding site. Overall, the results of in vitro studies and molecular modeling indicate that diquercetin competes with nicotinamide adenine dinucleotide (NAD+), whereas 2-chloro-1,4-naphthoquinone-quercetin competes with the acetylated substrate in the catalytic site of SIRT6. Natural polyphenolic compounds targeting sirtuins show promise as a new approach in the search for novel and effective treatments for age-related diseases.