The low-temperature thermal conductance of single-walled carbon nanotubes has been revealed by theoretical analysis based on the Landauer theory for thermal transports. The phonon-derived thermal conductance is quantized as a universal value of 4π²k²_BT/3h in the low-temperature limit, independent of their radii and chiralities. The temperature range where the quantization is observable increases as the tube-radius decreases. For metallic carbon nanotubes, an electronic contribution to thermal conductance is also quantized as the same value as that of phonon in the low-temperature limit and becomes negligibly small compared with a phonon contribution as temperature increases. We also discuss the thermal transport properties of graphitic ribbons as a potential wiring material in nanoscale electronic devices as well as carbon nanotubes.