We study the mechanical dissipation of the fundamental mode of millimeter-sized, high quality-factor (Q) metalized silicon nitride membranes at temperatures down to 14?mK using a three-dimensional optomechanical cavity. Below 200?mK, high-Q modes of the membranes show a diverging increase of Q with decreasing temperature, reaching Q=1.27×108Q=1.27×108 at 14?mK, an order of magnitude higher than that reported before. The ultra-low dissipation makes the membranes highly attractive for the study of optomechanics in the quantum regime, as well as for other applications of optomechanics such as microwave to optical photon conversion