Thin films of indium oxide and indium tin oxide have been prepared by d.c. magnetron sputtering onto the fused silica substrates kept at 90, 200 and $300^{circ}C$. In order to elucidate the optical absorption process in low energy region below 3 eV, we have analyzed the absorption coefficients obtained from reflectance and transmittance measurements for these films based on the Lucovsky model. It has been found for the first time that a defect center in the band gap is located at 0.8~1.4 eV below the Fermi level in all films and arises from oxygen vacancies in their films. The optical absorption in low energy region is explained to be dominated by the transition of electrons trapped at the positively charged (+2e) oxygen vacancies with s-like nature to the conduction band formed from the 5s-orbit in indium atoms.