Skin wound healing is one of the most challenging processes for skin reconstruction, especially after severe injuries. In our study, nanofiber membranes were prepared for wound healing using an electrospinning process, where the prepared nanofibers were made of different weight ratios of polycaprolactone and bioactive glass that can induce the growth of new tissue. The membranes showed smooth and uniform nanofibers with an average diameter of 118 nm. FTIR and XRD results indicated no chemical interactions of polycaprolactone and bioactive glass and an increase in polycaprolactone crystallinity by the incorporation of bioactive glass nanoparticles. Nanofibers containing 5% w/w of bioactive glass were selected to be loaded with atorvastatin, considering their best mechanical properties compared to the other prepared nanofibers (3, 10, and 20% w/w bioactive glass). Atorvastatin can speed up the tissue healing process, and it was loaded into the selected nanofibers using a dip-coating technique with ethyl cellulose as a coating polymer. The study of the in vitro drug release found that atorvastatin-loaded nanofibers with a 10% coating polymer revealed gradual drug release compared to the non-coated nanofibers and nanofibers coated with 5% ethyl cellulose. Integration of atorvastatin and bioactive glass with polycaprolactone nanofibers showed superior wound closure results in the human skin fibroblast cell line. The results from this study highlight the ability of polycaprolactone-bioactive glass-based fibers loaded with atorvastatin to stimulate skin wound healing.