In this study, silver nanoparticles (AgNPs) were synthesized via a green method from pomegranate peel extract and incorporated into polyvinyl alcohol (PVA) to produce AgPVA nanofibers through electrospinning. Nanofibers containing different silver concentrations (0.5, 1, and 1.5% Ag) were used as coating materials to coat minced meat, and their effects on various quality parameters during storage at 4 °C were evaluated. FTIR, XRD, SEM, and antibacterial analyses were conducted for the characterization of AgNPs and AgPVA nanofibers. To assess the quality characteristics of the minced meat during storage, pH, color, peroxide, TBARS, and microbiological analyses were performed. The results indicated that silver concentrations up to 1% could delay oxidation in minced meat and help preserve its quality. Compared with the other samples, the samples coated with 0.5% AgPVA (A1) and 1.0% AgPVA (A2) nanofibers exhibited a significant antimicrobial effect at the 6-day storage point (p < 0.05). The migration of AgNPs into minced meat was monitored during storage, and all migration values remained below the European food safety authority (EFSA) safety limit of 0.05 mg/kg, demonstrating the safety of the coatings. These findings suggest that AgPVA nanofibers synthesized via a green method could be a promising approach for extending the shelf life of perishable foods by reducing spoilage.