This study aims at preparing electrospun chitosan/gelatin nanofiber scaffolds reinforced with different amounts of graphene nanosheets to be used as antibacterial and wound-healing scaffolds. Full characterization was carried out for the different fabricated scaffolds before being assessed for their antimicrobial activity against Escherichia coli and Staphylococcus aureus, cytotoxicity, and cell migration capacity. Raman and transmission electron microscopies confirmed the successful reinforcement of nanofibers with graphene nanosheets. Scanning electron microscopy and porosity revealed that nanofibers reinforced with 0.15% graphene nanosheets produced the least diameter (106 ± 30 nm) and the highest porosity (90%), in addition to their good biodegradability and swellability. However, the excessive increase in graphene nanosheet amount produced beaded nanofibers with decreased porosity, swellability, and biodegradability. Interestingly, nanofibers reinforced with 0.15% graphene nanosheets showed E. coli and S. aureus growth inhibition percents of 50 and 80%, respectively. The cell viability assay showed no cytotoxicity on human fibroblasts when cultured with either unreinforced or reinforced nanofibers. The cell migration was higher in the case of reinforced nanofibers when compared to the unreinforced nanofibers after 24 and 48 h, which is substantially associated with the great effect of the graphene nanosheets on the cell migration capability. Unreinforced and reinforced nanofibers showed cell migration results up to 93.69 and 97%, respectively, after 48 h.