ZnMgO nanowires are synthesized on Si substrates using a vapor-transport method and their structural and luminescent characteristics are investigated using various techniques. The shift of the (002) peak in the X-ray diffraction measurements and the blue shift of the near-band-edge emission peak in the photoluminescence measurements of the ZnMgO samples are consistent with the incorporation of the small amount of Mg ($5 at.%) in ZnO. Individual ZnMgO nanowires are also investigated for their structural and luminescent properties, which show smaller amount of Mg incorporation ($1 at.%) into ZnO nanowires than in the case of ensemble of ZnMgO samples.