In this work, Cu NPs were loaded at a fixed percentage (5 wt%) on 1D, (1D + 0D) and 0D ZnO nanostructures to investigate the effect of the support morphology on the reduction of organic pollutants in water. The synthesized materials were characterized by high-resolution transmission electron microscopy (HR-TEM), ultraviolet-visible spectroscopy (UV-Vis), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), N adsorption-desorption and X-ray photoelectron spectroscopy (XPS). The results reveal that the loading of Cu NPs decreases the optical band gap, and a slight change in the crystallite sizes increases the specific surface area value of the nanocomposites. The TEM images reveal that 1D ZnO has an average width of 44.7 nm and an average length of 211 nm, while 0D ZnO has an average diameter of 54.5 nm. The HR-TEM and XPS data confirm the loading of metallic Cu NPs on the surface of the ZnO nanostructures. The pure ZnO and nanocomposites were tested for 4-nitrophenol (4-NP) reduction in the presence of NaBH at room temperature. The obtained results show that pure ZnO nanostructures have no catalytic performance, while the nanocomposites showed good catalytic activities. The catalytic reduction efficiency of 4-NP was found to follow the order of Cu/0DZnO > Cu/(1D + 0D)ZnO > Cu/1DZnO. The complete reduction of 4-NP has been observed to be achievable within 60 s using the Cu/0DZnO nanocomposite, with a value of 8.42 min and good recyclability of up to five cycles. This nanocomposite was then applied in the reduction of organic dyes in water; it was found that the reduction rate constants for the methylene blue, Congo red, and acriflavine hydrochloride dyes were 1.4 min, 1.2 min, and 3.81 min, respectively. The high catalytic performance of this nanocomposite may be due to the small particle size, high specific surface area, and the high dispersion of Cu NPs on the surface of ZnO.