ZnO micro-/nanostructures were synthesized by the carbothermal reduction–chemical vapour transport method. This work is focused on the effect of the substrate temperature and Cu catalyst layer on the shape and geometry of ZnO micro-/nanostructures. The thermally oxidized Cu template affects the structure, chemical identity, optical and photoluminescence properties of the ZnO micro-/nanostructure and results in a CuOx/ZnO heterostructure. SEM studies give a direct evidence of the role of deposition temperature and Cu catalyst in the formation of a stable hemisphere based wire, a comb-like cantilever, a javelin-like tetrapod, a spherical and polyhedral cage of ZnO. XRD and Raman measurements confirm a hexagonal wurtzite structure of the ZnO micro-/nanostructure. The absorption edge of the ZnO/CuOx heterostructure is redshifted in comparison to the pure ZnO structure. PL studies indicate that the UV emission can be suppressed significantly while the green emission is enhanced due to the change in the morphology of ZnO micro-/nanostructures.