Nanofibers can play an important role in developing new kinds of medical applications. Poly(lactic acid) (PLA) and PLA/poly(ethylene oxide) (PEO) antibacterial mats containing silver nanoparticles (AgNPs) were prepared by a simple one-step electrospinning method that allows AgNPs to be synthesized simultaneously with the preparation of the electrospinning solution. The electrospun nanofibers were characterized by scanning electron microscopy, transmission electron microscopy and thermogravimetry, while silver release over time was monitored by inductively coupled plasma/optical emission spectroscopy. The antibacterial activity was tested against Staphylococcus epidermidis and Escherichia coli by colony forming unit (CFU) count on agar after 15, 24 and 48 h of incubation. AgNPs were found to be mainly concentrated in the PLA nanofiber core, and the mats showed steady but slow Ag release in the short term; in contrast, AgNPs were uniformly distributed in the PLA/PEO nanofibers, which released up to 20% of their initial silver content in 12 h. A significant (p < 0.05) antimicrobial effect towards both tested bacteria, highlighted by a reduction in the CFU/mL counts, was observed for the nanofibers of PLA and PLA/PEO embedded with AgNPs, with a stronger effect exerted by the latter, confirming the more efficient silver release from these samples. The prepared electrospun mats may have good potential for use in the biomedical field, particularly in wound dressing applications, where a targeted delivery of the antimicrobial agent is highly desirable to avoid infections.