This study describes the design and synthesis of organic–inorganic hybrid hydrogels based on an interpenetrating polymer network (IPN) composed of polyaspartic acid crosslinked by graphene nanosheets as the primary network and poly(acrylamide-co-acrylic acid) as the secondary network. Silver, copper oxide, and zinc oxide nanoparticles were formed within the gel matrix, and the obtained hydrogel was applied to a load and controlled release of curcumin. The loading of curcumin and the release of this drug from the gels depended on the nanoparticle’s (NP’s) content of hydrogels as well as the pH of the medium. The synthesized hydrogels showed antibacterial activity against E. coli and S. aureus bacteria. The ability of the synthesized hydrogels to incapacitate bacteria and their loading capacity and controlled release of curcumin qualify them for future therapies such as wound-dressing applications.