The aim of this study was to determine the potential pharmaceutical applications of quercetin—a natural flavonoid compound with a polyphenolic structure—following its encapsulation in polymeric microspheres resistant to degradation. The microspheres were prepared from natural polymeric compounds (chitosan and sodium alginate) via a complex coacervation method, with the goal of protecting quercetin from the degradation reactions that can affect its bioactivity. After the microspheres were prepared, they were characterized using various analytical methods. The encapsulation efficiency (EE (%)), swelling index (idxSWL%), roughness (measured using confocal laser scanning microscopy—CLSM), and surface morphology (measured using scanning electron microscopy—SEM) were all analyzed. In addition, the release capacity of quercetin from the microspheres (mQrel%) and the antimicrobial activity of the microspheres were evaluated in vitro. Finally, a multivariate statistical analysis (MANOVA, p = 0.05, PCA, and AHC) was conducted. This analysis showed that chitosan–sodium alginate–quercetin microspheres (CAQ-Ms) entrap 86.91 ± 1.10–93.11 ± 0.72% quercetin; in vitro, 71.46 ± 0.25–91.06 ± 0.15% quercetin was released, and the swelling index was higher (6701.29 ± 0.39–10,009.30 ± 1.11%) in the phosphate-buffered solution with a pH of 7.4. The CLSM and SEM analyses showed that the polymer concentration in CAQ-Ms was increased, and the roughness and smoothness of the microspheres were also increased. SEM also showed that the external layer of CAQ-Ms was formed from chitosan and the internal layer was formed from sodium alginate. Antimicrobial tests showed that CAQ-Ms had antibacterial and antifungal effects on the analyzed strains and produced larger inhibition zones between 15.3 and 14.4 mm on Escherichia coli and between 13.3 and 14.2 mm on Candida albicans, and smaller inhibition zones, between 12.4 and 13.6 mm, on Staphylococcus aureus. According to the obtained results, after the multivariate statistical analysis, it can be observed that the best performance was presented by samples P1, P2, and P3. In conclusion, the method used for the formulation of CAQ-Ms was efficient because it enabled an increase in the solubility of quercetin in water and its protection against external and internal degradation in the gastrointestinal tract. This system can be further used to produce new pills for oral administration that are able to reach the small intestine, where they can then release loaded active drugs.