The onset of optical absorption in In2O3 at about 2.7 eV is investigated by transmission spectroscopy of single crystals grown from the melt. This absorption is not defect related but is due to the fundamental band gap of In2O3. The corresponding spectral dependence of the absorption coefficient is determined up to α = 2500 cm−1 at a photon energy hν = 3.05 eV at room temperature without indication of saturation. A detailed analysis of the hν dependence of α including low‐temperature absorption data shows that the absorption process can be well approximated by indirect allowed transitions. It is suggested that the fundamental band gap of In2O3 is of indirect nature. The temperature dependence of the fundamental band gap is measured over a wide range from 9 to 1273 K and can be well fitted by a single‐oscillator model. Compared to other semiconductors the reduction of the gap with increasing temperature is exceptionally strong in In2O3.