By studying the optical conductivity of Bi(2)Sr(2-x)La(x)CuO(6) and Y(0.97)Ca(0.03)Ba(2)Cu(3)O(6), we show that the metal-to-insulator transition in these hole-doped cuprates is driven by the opening of a small gap at low T in the far infrared. Its width is consistent with the observations of angle-resolved photoemission spectroscopy in other cuprates, along the nodal line of the k space. The gap forms as the Drude term turns into a far-infrared absorption, whose peak frequency can be approximately predicted on the basis of a Mott-like transition. Another band in the midinfrared softens with doping but is less sensitive to the metal-to-insulator transition.