Under the illumination of intense off-resonant laser light, the electronic states of semiconductors are strongly modified, or dressed, by the oscillating electric field. We present a framework using linear combination of atomic orbital band theory to calculate the dressed band structure and optical absorption spectrum of covalent semiconductors in an intense off-resonant laser field. The interaction with the laser field is taken into account exactly from the beginning of the band calculation. It is shown that the irradiation of an intense infrared laser gives rise to a blueshift of the absorption edge as well as the emergence of a new absorption band below the edge, in agreement with recent experimental data for GaAs crystals.