In this theoretical study, the electronic, structural, and optical properties of copper-doped zinc oxide (CZO) were investigated using the full-potential linearized enhanced plane wave method (FP-LAPW) based on the density functional theory (DFT). The Tran–Blaha modified Becke–Johnson exchange potential approximation (TB-mBJ) was employed to enhance the accuracy of the electronic structure description. The introduction of copper atoms as donors in the ZnO resulted in a reduction in the material’s band gap from 2.82 eV to 2.72 eV, indicating enhanced conductivity. This reduction was attributed to the Co-3d intra-band transitions, primarily in the spin-down configuration, leading to increased optical absorption in the visible range. The Fermi level of the pure ZnO shifted towards the conduction band, indicating metal-like characteristics in the CZO. Additionally, the CZO nanowires displayed a significant blue shift in their optical properties, suggesting a change in the energy band structure. These findings not only contribute to a deeper understanding of the CZO’s fundamental properties but also open avenues for its potential applications in optoelectronic and photonic devices, where tailored electronic and optical characteristics are crucial. This study underscores the significance of computational techniques in predicting and understanding the behavior of doped semiconductors, offering valuable insights for the design and development of novel materials for advanced electronic applications.