To neutralise the influence of the surface of ZnO nanowires for photonics and optoelectronic applications, we have covered them with insulating MgO film and individually contacted them for electrical characterisation. We show that such a metal-insulator-semiconductor-type nanodevice exhibits a high diode ideality factor of 3.4 below 1 V. MgO shell passivates ZnO surface states and provides confining barriers to electrons and holes within the ZnO core, favouring excitonic ultraviolet radiative recombination, while suppressing defect-related luminescence in the visible and improving electrical conductivity. The results indicate the potential use of ZnO/MgO nanowires as a convenient building block for nano-optoelectronic devices.