Wound dressings have long been used to promote the healing of skin injuries. In the work reported here, fibrous membranes were produced by electrospinning poly(N-vinylpyrrolidone) (PVP) solutions containing silver nitrate at varying mass ratios (1:200, 1:100 and 1:50 AgNO3:PVP). PVP solutions without AgNO3 were used as a control. The electrospun membranes were irradiated using 254 nm UV light to simultaneously photo-crosslink PVP and promote the formation of silver nanoparticles (AgNPs). The formation of AgNPs was confirmed by scanning electron microscopy and transmission electron microscopy, as well as by detecting the surface plasmon resonance peak at 420 nm in the UV–Vis spectrum during release studies. The swelling rate of fibrous membranes was lower for those containing AgNPs compared to PVP-only membranes. The Kirby-Bauer diffusion test performed against Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus, Staphylococcus epidermidis and Candida albicans showed that all AgNPs-containing membranes exhibited an inhibitory effect on all microorganisms tested. The in vitro cytotoxicity assay showed that membranes with lower silver concentration were less cytotoxic. This study presents a simple route to producing a wound dressing with antimicrobial action that has a swelling behavior capable of absorbing exudates, provides controlled release of silver and has low cytotoxicity.