We report the anisotropic changes in the electronic structure of a Kondo semiconductor CeOs(2)Al(10) across an anomalous antiferromagnetic ordering temperature (T(0)) of 29 K, using optical conductivity spectra. The spectra along the a and c axes indicate that an energy gap due to the hybridization between conduction bands and nearly local 4f states, namely the c-f hybridization gap, emerges from a higher temperature continuously across T(0). Along the b axis, on the other hand, another energy gap with a peak at 20 meV becomes visible at 39 K (>T(0)) and fully opens at T(0) because of a charge instability. This result implies that the appearance of the energy gap, as well as the change in the electronic structure along the b axis, induces the antiferromagnetic ordering below T(0).