We report on an approach to fabricate ZnTe-based core/shell radial heterostructures containing ZnO, as well as on some of their physical properties. The molecular beam epitaxy grown ZnTe nanowires constituted the core of the investigated structures and the ZnO shells were obtained by thermal oxidation of ZnTe NWs. The influence of the parameters characterizing the oxidation process on selected properties of core/shell NWs were examined. Scanning electron microscopy revealed changes of the NWs morphology for various conditions of the oxidation process. X-ray diffraction, high resolution transmission electron microscopy, and Raman scattering measurements were applied to reveal the presence of ZnTe single crystal core and polycrystalline ZnO-shell of investigated structure.