One-dimensional nanostructures, such as nanorod (NR) arrays, are expected to improve the photovoltaic (PV) response of solar cells with an ultrathin absorber due to an increased areal (junction) density and light trapping. We report on the deposition of CdS and CdTe:As semiconductor thin films on ZnO NR arrays by means of metalorganic chemical vapour deposition (MOCVD). The change in optical properties of the ZnO NRs upon the growth of CdS shell was monitored and compared to the simulated data, which confirmed the presence of strong light scattering effects in the visible and near infrared regions. The PV performance of nanostructured vs. planar CdS/CdTe solar cells (grown using the material from the same MOCVD run) showed similar conversion efficiencies (similar to 4%), despite the current density being lower for the nanostructured cell due to its thicker CdS window. A clear improvement in the quantum efficiency was however observed in the near infrared region, resulting from the light trapping by the ZnO/CdS core-shell NR structure. We also showed that reduction of surface defects and use of high absorber carrier density would boost the efficiency beyond that of planar CdTe solar cells. The reported device performance and the direct observation of light trapping are promising towards optimisation of extremely-thin-absorber CdTe PV devices.