  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.
