Recently, there has been increased interest in melanins, representatives of the class of condensed polyphenols that find wide practical applications in various industries. In this study, melanin was isolated from the endophytic fungus Cladosporium sp.-HT207, and a polymer nanocomposite was developed based on melanin, using carboxymethylcellulose as a matrix. The structure and physicochemical properties of the nanocomposite films were studied using FTIR spectroscopy, X-ray diffraction, thermal analysis, atomic force microscopy, and mechanical testing. The antibacterial, antifungal, anti-inflammatory, and antioxidant activities of the nanocomposite films were also investigated. It has been found that films containing 0.15% of melanin nanoparticles exhibit relatively high anti-inflammatory and antioxidant activities. The resulting nanocomposite films may have applications in biomedicine, pharmaceuticals, and cosmetology.