Staphylococcus aureus is a pathogen widely involved in wound infection due to its ability to release several virulence factors that impair the skin healing process, as well as its mechanism of drug resistance. Herein, sodium alginate and chitosan were combined to produce a hydrogel for topical delivery of neomycin to combat S. aureus associated with skin complications. The hydrogel was formulated by combining sodium alginate (50 mg/mL) and chitosan (50 mg/mL) solutions in a ratio of 9:1 (HBase). Neomycin was added to HBase to achieve a concentration of 0.4 mg/mL (HNeo). The incorporation of neomycin into the product was confirmed by scanning electron microscopy, FTIR and TGA analysis. The hydrogels produced are homogeneous, have a high swelling capacity, and show biocompatibility using erythrocytes and fibroblasts as models. The formulations showed physicochemical and pharmacological stability for 60 days at 4 ± 2 °C. HNeo totally inhibited the growth of S. aureus after 4 h. The antimicrobial effects were confirmed using ex vivo (porcine skin) and in vivo (murine) wound infection models. Furthermore, the HNeo-treated mice showed lower severity scores than those treated with HBase. Taken together, the obtained results present a new low-cost bioproduct with promising applications in treating infected wounds.