Mg-doped ZnO one-dimensional (1D) nanostrutures were synthesized by using a thermal evaporation technique. The morphology, crystal structure, and sensing properties of the Mg-doped ZnO nanostructures functionalized with Pt to CO gas at $100^{circ}C$ were examined. The diameters of the 1D nanostructures ranged from 80 to 120 nm and that the lengths were up to a few tens of micrometers. The gas sensors fabricated from multiple networked Mg-doped ZnO nanowires functionalized with Pt showed enhanced electrical response to CO gas. The responses of the nanowires were improved by approximately 70, 69, 111, and 81 times at CO concentrations of 10, 25, 50, and 100 ppm, respectively. Both the response and recovery times of the nanowire sensor for CO gas sensing were not nearly changed by Pt functionalization. It also appeared that the Mg doping concentration did not influence the sensing properties of ZnO nanowires as strongly as Pt-functionalization. In addition, the mechanism for the enhancement in the CO gas sensing properties of Mg-doped ZnO nanowires by Pt functionalization is discussed.