We have determined by means of optical-absorption experiments that Fe(IO3)3 is an indirect band-gap material with a band-gap energy of 2.1 eV. This makes this compound the iodate with the smallest band gap. We also found that under compression the band-gap energy has an unusual non-linear pressure dependence, which is followed by an abrupt and discontinuous decrease of the band gap at 24 GPa. The observed behavior is explained by means of density-functional calculations, which show that the behavior of the band gap is governed by the combined influence of Fe 4d and I 5p lone pair electrons. In addition, the abrupt decrease of the band-gap energy at 24 GPa is a consequence of a first-order structural phase transition. These conclusions are confirmed by resistivity measurements, which show that intrinsic carriers dominate the transport properties of Fe(IO3)3.