The rising levels of water pollution and climate change contribute to water shortages. These factors influence the loss of the environment’s biodiversity and threaten human health. Toxic dye pigments from industries are a significant source of pollution. In this article, we present the synthesis method, characteristics, and photocatalytic properties of the CuO-ZnO nanocomposite, which may affect the degree of decomposition of dyes found in water. The nanocomposite consisting of copper oxide nanowires with zinc oxide nanostructures (CuO-ZnO nanocomposite) was prepared by physical vapor deposition and thermal oxidation methods. The crystalline structure, surface topographies and morphologies, elemental composition, and optical properties of the obtained samples were studied with various techniques such as x-ray diffraction analysis, high-resolution transmission electron microscopy, field emission scanning electron microscopy, energy dispersive x-ray analysis, and UV-vis spectroscopy. The photocatalytic activity of the nanocomposite was measured by testing the degradation of methylene blue under visible irradiation. An increase in the photocatalytic activity of the nanocomposite was observed compared to pure CuO and ZnO. The CuO-ZnO nanocomposite demonstrated a high dye degradation of about 94% during 120 min.