Antibacterial and cyto-compatible tricomponent composite electrospun nanofibers comprised of polyvinyl alcohol (PVA), copper II oxide nanoparticles (CuONPs), and Momordica charantia (bitter gourd, MC) extract were examined for their potential application as an effective wound dressing. Metallic nanoparticles have a wide range of applications in biomedical engineering because of their excellent antibacterial properties; however, metallic NPs have some toxic effects as well. The green synthesis of nanoparticles is undergoing development with the goal of avoiding toxicity. The aim of adding Momordica charantia extract was to reduce the toxic effects of copper oxide nanoparticles as well as to impart antioxidant properties to electrospun nanofibers. Weight ratios of PVA and MC extract were kept constant while the concentration of copper oxide was optimized to obtain good antibacterial properties with reduced toxicity. Samples were characterized for their morphological properties, chemical interactions, crystalline structures, elemental analyses, antibacterial activity, cell adhesion, and toxicity. All samples were found to have uniform morphology without any bead formation, while an increase in diameters was observed as the CuO concentration was increased in nanofibers. All samples exhibited antibacterial properties; however, the sample with CuO concentration of 0.6% exhibited better antibacterial activity. It was also observed that nanofibrous mats exhibited excellent cytocompatibility with fibroblast (NIH3T3) cells. The mechanical properties of nanofibers were slightly improved due to the addition of nanoparticles. By considering the excellent results of nanofibrous mats, they can therefore be recommended for wound dressing applications.