This study aimed to prepare a polyvinyl alcohol/sodium alginate (PVSA) nanofibrous mat as an amoxicillin (AMOX) delivery system. AMOX was loaded to the PVSA nanofibers during electrospinning, and the AMOX-loaded PVSA (PVSA/AMOX) nanofibrous mat was cross-linked by glutaraldehyde (GA). The PVSA/AMOX nanofibrous mat was characterized by Fourier Transform infrared spectroscopy, scanning electron microscopy, Brunauer–Emmett–Teller, and mercury porosimetry analyses. The thickness, air permeability, and water vapor transmission rate of the PVSA/AMOX nanofibrous mat were 0.43 ± 0.08 mm, 17.2 ± 4.91 L/m²/s, and 1485 ± 13.6 g/m²/d, respectively, which were suitable for wound dressing applications. The tensile strength was 6.73 ± 0.48 MPa and elongation at a maximum load was 81.9 ± 17.0%, within the ranges of human skin’s values. The total porosity was 59.4%, enabling cell adhesion, migration, and proliferation. The PVSA/AMOX nanofibrous mat has high swelling (319 ± 4.2%) and low degradation (2.2 ± 0.1% in 10 days) ratios. The nanofibrous mat cross-linked with 0.25% GA solution for 20 min had a 73.07% cumulative release for 90 min. The drug release kinetics were obeyed to the Korsmeyer-Peppas model. The nanofibrous mat presented antibacterial activity on S. aureus ATCC 29213 and E. coli ATCC 25922, and there was no cytotoxic effect on the human normal keratinocyte cells, demonstrating the potential for use in wound dressing applications.