Methods of synthesis and growth of good quality, uniaxial In-4(P2Se6)(3) single crystals were developed. The temperature dependence of the optical absorption edge of these crystals was studied at high absorption levels in the spectral range of direct optical transitions. At low temperatures, we observed an exciton band corresponding to the optical absorption with the formation of direct s-excitons. In the long-wavelength spectral range of the absorption edge, Urbach tails were observed. We showed that the exponential dependence of absorption coefficient on photon energy is a consequence of exciton-phonon interaction, whose mechanism is explained within the framework of Dow-Redfield theory. The influence of disorder on the width of Urbach tails was analyzed as well.