Biogenic metal oxide nanoparticles (NPs) have emerged as a useful tool in biology due to their biocompatibility properties with most biological systems. In this study, we report the synthesis of copper oxide (CuO), zinc oxide (ZnO) nanoparticles (NPs), and their nanocomposite (CuO–ZnO) prepared using the phytochemical extracts from the leaves of Dovyalis caffra (kei apple). The physicochemical properties of these nanomaterials were established using some characterization techniques including X-ray diffraction analysis (XRD), ultraviolet-visible spectroscopy (UV-vis), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy-dispersive X-ray spectroscopy (EDX). The XRD result confirmed the presence of a monoclinic CuO (Tenorite), and a hexagonal ZnO (Zincite) nanoparticles phase, which were both confirmed in the CuO–ZnO composite. The electron microscopy of the CuO–ZnO, CuO, and ZnO NPs showed a mixture of nano-scale sizes and spherical/short-rod morphologies, with some agglomeration. In the constituent’s analysis (EDX), no unwanted peak was found, which showed the absence of impurities. Antioxidant properties of the nanoparticles was studied, which confirmed that CuO–ZnO nanocomposite exhibited better scavenging potential than the individual metal oxide nanoparticles (CuO, and ZnO), and ascorbic acid with respect to their minimum inhibitory concentration (IC50) values. Similarly, the in vitro anticancer studies using MCF7 breast cancer cell lines indicated a concentration-dependent profile with the CuO–ZnO nanocomposite having the best activity over the respective metal oxides, but slightly lower than the standard 5-Fluorouracil drug.