Optical conductivity data of the intermetallic compounds (Fe1-xVx)3Al ( 0</=x</=0.33) reveal that their density of states around the Fermi energy ( E(F)) is strongly reduced as x is increased. In particular, Fe2VAl ( x = 0.33) has a deep, well-developed pseudogap of 0.1-0.2 eV at E(F) and a small density ( approximately 5x10(20) cm(-3)) of carriers, which is highly unusual for intermetallic compounds. It is shown that the pseudogap results from the band structure of Fe2VAl, rather than from temperature-dependent correlation effects. Based on the present results, we propose a simple model that consistently explains both the semiconductorlike transport and the metallic photoemission results previously observed for Fe2VAl.