Bio-nanocomposite hydrogels based on sodium alginate (SA) as polymer matrix and graphene oxide (GO) nanosheets with zinc as crosslinking agent were synthesized with the aim of incorporating the intrinsic properties of their constituents (bioactivity and antimicrobial activity). Thus, stable and highly interconnected networks were obtained from GO nanosheets dispersed in SA matrices through interactions with low amounts of zinc. The GO nanosheets were successfully incorporated into the alginate matrix in the form of a complex nano-network involving different interactions: Bonds between alginate chains induced by Zn ions (egg box structure), interactions between GO nanosheets through Zn ions and hydrogen bonds between alginate chains, and GO nanosheets. The molecular interactions and morphology were confirmed by Fourier-transform infrared spectroscopy and transmission electron microscopy. The composite’s structural organization showed enhanced thermal stability. The glass transition temperature shifted to a higher temperature due to the reduced mobility induced by additional crosslinking bonds after incorporating the GO nanosheets and Zn into the polymer matrix. Finally, the dielectric behavior revealed that charge carrier mobility was hampered by the compact structure of the nanonetwork, which reduced conductivity. The combined properties of these nanocomposite hydrogels make them attractive biomaterials in the field of regenerative medicine and wound care since both surface bioactivity and antibacterial behavior are two critical factors involved in the success of a biomaterial.