Diclofenac sodium salt (DSS)-loaded electrospun nanofiber mats on the base of poly(ε-caprolactone) (PCL) were investigated as biocompatible nanofibrous mats for medical applications with the ability to inhibit bacterial infections. The paper presents the characteristics of fibrous mats made by electrospinning and determines the effect of medicament on the fiber morphology, chemical, mechanical and thermal properties, as well as wettability. PCL and DSS-loaded PCL nanofibrous mats were characterized using scanning electron microscopy, transmission electron microscopy, attenuated total reflectance-Fourier transform infrared spectrometry, dynamic mechanical analysis, and contact angle measurements. Electron paramagnetic resonance measurements confirmed the lifetime of DSS before and after application of high voltage during the electrospinning process. In vitro biocompatibility was studied, and it was proved to be of good viability with ~92% of the diploid human cells culture line composed of lung fibroblast (MRC 5) after 48 h of incubation. Moreover, the significant activity of DSS-loaded nanofibers against cancer cells, Ca Ski and HeLa, was established as well. It was shown that 12.5% (m/V) is the minimal concentration for antibacterial activity when more than 99% of Escherichia coli (Gram-negative) and 99% of Staphylococcus aureus (Gram-positive) have been exterminated.