Glow discharge plasma was implemented to reveal the effect caused by ions extracted from plasma and accelerated in DC plasma sheath with respect to the synthesis of copper oxide nanostructures of different dimensionality (2D and 3D). For the purpose, a copper cap with a small orifice in the upper part was employed to cover a part of a surface of a disk-shaped copper sample, while another part was left exposed to the ion fluxes accelerated across the voltage drop of 760 V. It was shown, that at the same temperature, the exposed area demonstrated a large yield of 2D and 3D nanostructures grown after 30 min in oxygen atmosphere maintained at the pressure of 360 Pa, while the surface treated with just neutral flux did not show any traces of nanostructures. Moreover, the intermediate case of the treatment with the flux where the active neutral plasma species were left after passing the plasma flux through the small aperture, while the most ions were removed, also resulted in the formation of 2D nanostructures yet at much lower yield than on the exposed to plasma area. The findings are important with respect to the development of a reliable, flexible, high-production and cost-effective technology of synthesis of metal oxide nanostructures of various morphology.