Topical drug delivery in skin diseases provides a non-invasive, direct application of treatments to the affected area and avoids systemic toxicity. Quercetin is a natural polyphenol with documented activity to alleviate the symptoms of many skin diseases. The objective of this study was to prepare and assess the physicochemical properties of hydrogels made of sodium alginate (SA) and cellulose derivatives (methyl cellulose (MC) and carboxymethyl cellulose (CMC)), containing different concentrations of quercetin (0.4 and 0.7%). The physicochemical evaluation of the obtained hydrogels included organoleptic evaluation, texture analysis, spreadability, rheological properties, pH, and stability. Among the prepared formulations, MC-based gels had the highest viscosity, adhesiveness, cohesiveness, and stickiness. The results of this study indicate that MC-based hydrogels were superior to CMC- or SA-based gels in their ability to effectively deliver quercetin to the porcine skin ex vivo. The amount of quercetin retained in the skin after application of MC-based preparations containing higher concentrations of quercetin was 2.04-fold higher for CMC-based hydrogels and 2.6-fold higher for SA-based hydrogels.