Novel eco-friendly fibrous materials with complex activities from cellulose acetate and cellulose acetate/polyethylene glycol (CA,PEG) containing 5-chloro-8-hydroxyquinoline as a model drug were obtained by electrospinning. Several methods, including scanning electron microscopy, X-ray diffraction analysis, ultraviolet-visible spectroscopy, water contact angle measurements, and mechanical tests, were utilized to characterize the obtained materials. The incorporation of PEG into the fibers facilitated the drug release. The amounts of the released drug from CA/5-Cl8Q and CA,PEG/5-Cl8Q were 78 ± 3.38% and 86 ± 3.02%, respectively (for 175 min). The antibacterial and antifungal activities of the obtained materials were studied. The measured zones of inhibition of CA/5-Cl8Q and CA,PEG/5-Cl8Q mats were 4.0 ± 0.18 and 4.5 ± 0.2 cm against S. aureus and around 4.0 ± 0.15 and 4.1 ± 0.22 cm against E. coli, respectively. The complete inhibition of the C. albicans growth was detected. The cytotoxicity of the obtained mats was tested toward HeLa cancer cells, SH-4 melanoma skin cells, and mouse BALB/c 3T3 fibroblasts as well. The CA/5-Cl8Q and CA,PEG/5-Cl8Q materials exhibited anticancer activity and low normal cell toxicity. Thus, the obtained fibrous materials can be suitable candidates for wound dressing applications and for application in local cancer treatment.