Quercetin (QC) has various biological activities such as anti-inflammatory and antibacterial properties. However, due to its poor solubility and stability, the application of QC in clinical practice is limited. Nanosponge (NS), as a new drug carrier, can significantly improve the solubility of low-soluble drug components, and significantly improve the efficacy and bioavailability of drugs. In this paper, cyclodextrin nanosponges (CDNS) were synthesized by cross-linking beta-cyclodextrin with diphenyl carbonate (DPC) in a green and safe synthetic pathway. As wall material, CDNS were further used to encapsulate quercetin and quercetin-cyclodextrin nanosponges (QCNS) were formed. The resultant CDNS and QCNS were characterized by scanning electron microscopy, infrared spectroscopy, X-ray diffraction, and thermogravimetric analysis. The results showed that CDNS and QCNS were successful prepared. The solubilizing impact of CDNS on quercetin was investigated. The results showed that its solubility in water was 176 times higher than that of pure QC. The cumulative release of quercetin and QCNS over 48 h and the cumulative transdermal penetration over 12 h were measured. The antioxidant and antibacterial properties of QCNS were determined. QCNS exhibited superior stability, permeability, and sustained-release properties compared to pure quercetin, and had notable bacteriostatic and antioxidant capabilities.