The absorption length, \(\lambda_{abs}\), of light with wavelengths between 0.95 and 1.30\(~\mu\)m in silicon irradiated with 24\(~\)GeV/c protons to 1\(~\)MeV neutron equivalent fluences between 0 and \(8.6 \times 10^{15}~\)cm\(^{-2}\) has been measured. It is found that \(\lambda_{abs}\) decreases with fluence due to radiation-induced defects. A phenomenological parametrisation of the radiation-induced change of \(\lambda_{abs}\) as a function of wavelength and neutron equivalent fluence at room temperature is given. The observation of the decrease of \(\lambda_{abs}\) with irradiation is confirmed by edge-TCT measurements on irradiated silicon strip detectors. Using the measured wavelength dependence of \(\lambda_{abs}\), the change of the silicon band-gap with fluence is determined.