Chronic or improperly healed wounds, either as a result of extended trauma or prolonged inflammatory response, affect a significant percentage of the world population. Hence, there is a growing interest in the development of biomimetic scaffolds that expedite wound closure at the early stages. Curcumin (Cur) is a plant-derived polyphenol with antimicrobial activity, and it accelerates the wound contraction rate. Recently, electrospraying has emerged for the precise deposition of bioactive molecules into scaffolds to improve therapeutic outcomes. In this study, we produced membranes for wound healing and endowed them with antibacterial properties to promote the healing of impaired wounds. Unlike previous studies that incorporated curcumin directly into electrospun fibers, we employed electrospraying to coat curcumin onto PVA/KC membranes. This approach improves the curcumin bioavailability and release kinetics, ensuring sustained therapeutic action. Toward this end, we fabricated four types of membranes, poly(vinyl alcohol) PVA and PVA/kappa carrageenan (KC), using electrospinning, and PVA/KC/Cur5 and PVA/KC/Cur20, in which the PVA/KC membranes were coated with two different concentrations of Cur by electrospraying. All membranes showed low cytotoxicity, good cell adhesion, the capability of enabling cells to produce collagen, and an adequate degradation rate for wound-healing applications. Antibacterial evaluation showed that both Cur-loaded membranes increased the antibacterial efficacy against both Escherichia coli and Staphylococcus aureus compared with PVA and PVA/KC membranes. These findings highlight the potential of electrosprayed curcumin as an effective strategy for bioactive wound dressings.