Currently, plant extract-mediated synthesized metal oxide nanoparticles (MO NPs) have played a substantial role in biological applications. Hence, this study focused on the eco-benign one-pot synthesis of bimetallic ZnO−CuO nanoparticles (ZC NPs) using the leaf extract of Artemisia abyssinica (LEAA) and evaluations of their anticancer, antioxidant, and molecular binding efficacy. The optical absorption peak at 380 nm from UV−visible (UV−vis) analysis revealed the formation of ZC NPs. X-ray diffraction (XRD) results revealed the fabrication of mixed-phase crystals with hexagonal and monoclinic structures of ZC NPs with an average crystallite size of 14 nm. Moreover, the biosynthesis of ZC NPs with a spherical morphology and an average particle size of 13.09 nm was confirmed by scanning electron microscopy (SEM), energy-dispersive X-ray (EDX), and transmission electron microscopy (TEM) results. Fourier transform infrared (FTIR) and thermogravimetric analysis (TGA/DTA) spectroscopy confirmed the involvement of functional groups from LEAA during the synthesis of ZC NPs. ZC NPs have exhibited the ferric ion reducing power (FRAP) with an absorbance of 1.826 ± 0.00 at 200 μg/ mL and DPPH (2,2-diphenyl-1-picryl-hydrazyl-hydrate) radical scavenging activity of 95.71 ± 0.02% at 200 μg/mL with an IC50 value of 3.28 μg/mL. Moreover, ZC NPs had shown a promising in vitro anticancer activity of 89.20 ± 0.038 at 500 μg/mL with an IC50 value of 33.12 μg/mL against breast cancer (MCF-7) cell lines. Likewise, ZC NPs have shown strong binding affinity (−8.50 kcal/mol) against estrogen receptor α (ERα) in molecular docking simulations. These findings suggested that the biosynthesized ZC NPs could be used as promising antioxidant and anticancer drug candidates, particularly for breast cancer ailments. However, the in vivo cytotoxicity test will be recommended to ensure further use of ZC NPs.