Impairment of the cutaneous wound healing process, particularly under conditions such as large wound size, infection, and inefficient tissue regeneration, can lead to the development of chronic wounds and pose serious health-threatening risks. In recent years, nanofibrous wound dressings with unique properties have attracted considerable attention as a novel strategy to enhance therapeutic efficacy while minimizing drug-related side effects. In the present study, poly(vinyl alcohol)/chitosan nanofibers loaded with azelaic acid were designed and fabricated for skin wound dressing applications. The nanofibers were produced via electrospinning, and their physicochemical properties, drug-release profile, degradation behavior, hemocompatibility, and cellular biocompatibility were systematically evaluated. The results demonstrated that azelaic acid loading up to 20 wt% led to the formation of uniform, and defect-free nanofibers with nanoscale diameters. The analysis confirmed favorable structural interactions between azelaic acid and the polymeric matrix. The prepared nanofibrous dressing exhibited a highly hydrophilic surface, high porosity, adequate fluid absorption capacity, and suitable mechanical strength for wound dressing applications. Furthermore, sustained drug release over 72 h, gradual degradation, excellent hemocompatibility, and a significant enhancement in fibroblast cell viability were observed. Overall, azelaic acid–loaded poly(vinyl alcohol)/chitosan nanofibers demonstrate considerable potential as a multifunctional wound dressing for accelerating cutaneous wound healing.