Hirsutism is a distressing condition that can affect women’s self-esteem due to the excessive amount of hair growth in different body parts, including the face. A temporary managing option is to develop a self-care routine to remove unwanted hair through shaving or waxing. Laser or electrolysis are alternative methods, but in some cases, the use of medications, such as the topical cream Vaniqa®, can help in reducing the growth of unwanted hair. Electrospun fibers have been used in several drug delivery applications, including skin care products, owing to their biocompatibility, biodegradability, high surface area-to-volume ratio, and dry nature that can release the encapsulated drugs with maximum skin penetration. Therefore, polyvinyl pyrrolidone (PVP) fibers were fabricated in combination with hyaluronic acid to deliver the active compound of Vaniqa®, i.e., Eflornithine hydrochloride (EFH), as a face mask to inhibit excess facial hair growth. The prepared drug-loaded fibers showed a diameter of 490 ± 140 nm, with an encapsulation efficiency of 88 ± 7% and a drug loading capacity of 92 ± 7 μg/mg. The in vitro drug release of EFH-loaded fibers exhibited an initial burst release of 80% in the first 5 min, followed by a complete release after 360 min, owing to the rapid disintegration of the fibrous mat (2 s). The in vitro cytotoxicity indicated a high safety profile of EFH at all tested concentrations (500–15.625 μg/mL) after 24-h exposure to human dermal fibroblast (HFF-1) cells. Therefore, this drug-loaded nanofibrous system can be considered a potentially medicated face mask for the management of hirsutism, along with the moisturizing effect that it possesses. Topical applications of the developed system showed reduced hair growth in mice to a certain extent.