The goal of this study is to obtain and characterize the complex of quercetin with glycyrrhizic acid, which is known to serve as a drug delivery system. Quercetin is a flavonoid with a wide range of biological activities, including an antimicrobial effect. However, quercetin instability and low bioavailability that limits its use in medical practice makes it necessary to look for new nanoformulations of it. The formation of the GAQ complex (2:1) was confirmed by using UV and FT-IR spectroscopies. It was found that the GAQ exhibited antimicrobial and antihemolytical activities against S. aureus bacteria and its main virulent factor—α-hemolysin. The IC₅₀ value for the antihemolytical effect of GAQ was 1.923 ± 0.255 µg/mL. Using a fluorescence method, we also showed that the GAQ bound tightly to the toxin that appears to underlie its antihemolytic activity. In addition, another mechanism of the antihemolytic activity of the GAQ against α-hemolysin was shown, namely, its ability to increase the rigidity of the outer layer of the erythrocyte membrane and thus inhibit the incorporation of α-hemolysin into the target cells, increasing their resistance to the toxin. Both of these effects of GAQ were observed at concentrations below the MIC value for S. aureus growth, indicating the potential of the complex as an antivirulence agent.