Electrospun polycaprolacyone/polymethacrylic acid graft copolymer nanofibers (PCL/MAA) containing silver nanoparticles (AgNPs) were synthesized for effective wound disinfection. Surface morphology, AgNPs content, water uptake of electrospun PCL/MAA graft copolymer nanofibers without and with AgNPs, and levels of AgNPs leaching from the nanofibers in water as well as antimicrobial efficacy were studied. Scanning electron microscope images revealed that AgNPs dispersed well in PCL/MAA copolymer nanofibers with mean fiber diameters in the range of 200–579 nm and the fiber uniformity and diameter were not affected by the AgNPs. TEM images showed that AgNPs are present in/on the electrospun PCL/MAA graft copolymer nanofibers. The diameter of the electrospun nanofibers containing AgNPs was in the range of 200–579 nm, however, the diameter of AgNPs was within the range of 20–50 nm and AgNPs were observed to be spherical in shape. The PCL/MAA copolymer nanofibers showed a good hydrophilic property and the nanofibers containing AgNPs had excellent antimicrobial activity against the Gram-negative bacteria Escherichia coli and Pseudomonas aeruginosa, and against the Gram-positive bacteria Bacillus thuringiensis and Staphylococcus aureus, with a clear inhibition zone with a diameter between 22 and 53 mm. Moreover, electrospun PCL/MAA copolymer nanofibers sustained the release of AgNPs into water over 72 h.