A new type of fibrous mat based on a cellulose derivative—cellulose acetate (CA) or CA and water-soluble polymers (polyvinylpyrrolidone, PVP or poly(vinyl alcohol), PVA)—loaded with the model drug 5-nitro-8-hydroxyquinoline (5N) was fabricated via electrospinning or electrospinning in conjunction with electrospraying. Scanning electron microscopy (SEM), X-ray diffraction analysis (XRD), Fourier-transform infrared spectroscopy (FTIR), water contact angle measurements and ultraviolet-visible spectroscopy (UV-Vis) were used for the complex characterization of the obtained novel material. The decoration of CA fibers with a water-soluble polymer containing the drug resulted in the facilitation of wetting and fast drug release. The 5N-containing fibrous material showed antioxidant activity. Moreover, the proposed materials’ antibacterial and antifungal properties were tested againstS. aureus,E. coli,P. aeruginosaandC. albicans. Well-distinguished, sterile zones with diameters above 3.5 cm were observed around all 5N-containing mats. The mats’ cytotoxicity toward HeLa carcinoma cells and normal mouse BALB/c 3T3 fibroblasts was assessed. The 5N-in-CA, PVP,5N-on-(5N-in-CA) and PVA,5N-on-(5N-in-CA) fibrous mats possessed anticancer efficacies and much lower levels of toxicity against normal cells. Therefore, the as-created novel electrospun materials, which are based on polymers loaded with the drug 5N via electrospinning/electrospraying, can potentially be applied for topical wound healing and for local cancer therapy.