Traditional wound dressings do not provide all the clinical demands due to the lack of multifunctionality. There is an increasing request for advanced wound dressings to treat severe injuries and manage infections. Bioactive nanofibrous mats based on polymers with antibacterial performance are desirable options for wound dressing applications. In this study, we fabricated nanofibrous mats composed of ALG/PVA/CIP/ZO by electrospinning. The prepared nanofibrous mats were characterized for morphology and chemical composition. The analysis demonstrated the presence of CIP and ZO in nanofibrous mats with a uniform and unbranched appearance and fiber diameters of around 100–130 nm. Then the degradation, swelling, WVTR, drug release, antibacterial, and biocompatibility tests were performed to investigate the nanofibrous mat’s potential as a wound dressing. The swelling and WVTR measurements confirmed the excellent ability of nanofibrous mats for exudate absorption and preventing their accumulation in the wound area. The drug release pattern showed the pH-sensitive release, which results in more drug release at higher pH (infected wounds). The results of antibacterial, degradation and TGA tests demonstrated that the ZO nanoparticles in fabricated nanofibrous mats not only increased the antibacterial activity but also reinforced the crosslinking of polymers, leading to more physical and thermal stabilities. Also, the CIP in nanofibrous mats caused impressive enhancement in antibacterial properties by up to 99%. Overall, the developed nanofibrous mat with both CIP and ZO can be a promising candidate for biocompatible wound dressings with excellent antibacterial properties.