In this paper, we report a method of growing of the catalyst-free self-organized ZnMgO nanocolumns with single quantum well on Si (111) substrates by plasma-assisted molecular beam epitaxy technique (PA-MBE). The structures were grown without buffer layers. Optical properties of the ZnMgO/ZnO/ZnMgO quantum wells were studied by photo (PL)- and cathodoluminescence (CL) spectroscopy. A detailed analysis of the optical properties has been carried out, including quantum confinement effect and temperature dependence of excitonic emission. The structures reveal intense near band edge emission in PL as well as in CL. Blue shift of excitonic emission from the wells in comparison to bulk ZnO due to the quantum confinement effect is observed. Cross-sectional SEM–CL mapping shows that the ZnO/ZnMgO single quantum wells with different well widths are located in ZnMgO nanocolumns. The crystalline quality of the heterostructure was characterized by X-ray diffraction (XRD). No phase separation in ZnO/ZnMgO quantum structures was found.