Burn injuries represent a major life-threatening event that impacts the quality of life of patients, and places enormous demands on the global healthcare systems. This study introduces the fabrication and characterization of a novel wound dressing made of core–shell hyaluronic acid–silk fibroin/zinc oxide (ZO) nanofibers for treatment of burn injuries. The core–shell configuration enables loading ZO—an antibacterial agent—in the core of nanofibers, which in return improves the sustained release of the drug and maintains its bioactivity. Successful formation of core–shell nanofibers and loading of zinc oxide are confirmed by transmission electron microscopy, Fourier-transform infrared spectroscopy, and energy dispersive X-ray. The antibacterial activity of the dressings are examined against Escherichia coli and Staphylococcus aureus and it is shown that addition of ZO improves the antibacterial property of the dressing in a dose-dependent fashion. However, in vitro cytotoxicity studies show that high concentration of ZO (>3 wt%) is toxic to the cells. In vivo studies indicate that the wound dressings loaded with ZO (3 wt%) substantially improves the wound healing procedure and significantly reduces the inflammatory response at the wound site. Overall, the dressing introduced herein holds great promise for the management of burn injuries.