CuO-ZnO core-shell radial heterojunction nanowire arrays were obtained by a simple route which implies two cost-effective methods: thermal oxidation in air for preparing CuO nanowire arrays, acting as a p-type core and RF magnetron sputtering for coating the surface of the CuO nanowires with a ZnO thin film, acting as a n-type shell. The morphological, structural, optical and compositional properties of the CuO-ZnO core-shell nanowire arrays were investigated. In order to analyse the electrical and photoelectrical properties of the metal oxide nanowires, single CuO and CuO-ZnO core-shell nanowires were contacted by employing electron beam lithography (EBL) and focused ion beam induced deposition (FIBID). The photoelectrical properties emphasize that the p-n radial heterojunction diodes based on single CuO-ZnO core-shell nanowires behave as photodetectors, evidencing a time-depending photoresponse under illumination at 520 nm and 405 nm wavelengths. The performance of the photodetector device was evaluated by assessing its key parameters: responsivity, external quantum efficiency and detectivity. The results highlighted that the obtained CuO-ZnO core-shell nanowires are emerging as potential building blocks for a next generation of photodetector devices.