A nanocomposite based on an antibiotic-loaded hydrogel into a nano-electrospun fibre with antimicrobial and antioxidant capacities is investigated. The material is composed of nanofibres of enzymatic PCL grafted with poly(gallic acid) (PGAL), a recently developed enzyme-mediated hydrophilic polymer that features a multiradical and polyanionic nature in a helicoidal secondary structure. An extensive experimental-theoretical study on the molecular structure and morphological characterizations for this nanocomposite are discussed. The hydrogel network is formed by sodium carboxymethylcellulose (CMC) loaded with the broad-spectrum antibiotic clindamycin. This nano electrospun biomaterial inhibits a strain of Staphylococcus aureus, which is the main cause of nosocomial infections. The SPTT assay demonstrates that PGAL side chains also improve the release rates for this bactericide owing to the crosslinking to the CMC hydrogel matrix. The absence of hemolytic activity and the viability of epithelial cells demonstrates that this nanocomposite has no cytotoxicity.