The hydrogenation of $AlB_2$-type BaGaGe exhibits a metal to insulator (MI) transition, inducing a puckering distortion of the original hexagonal [GaGe] layers. We investigate the electronic structure changes associated with the hydrogen-induced MI transition, using extended H$ddot{u}$ckel tight-binding band calculations. The results indicate that hydrogen incorporation in the precursor BaGaGe is characterized by an antibonding interaction of $pi$ on GaGe with hydrogen 1s and the second-order mixing of the singly occupied antibonding $pi^*$ orbital into it, through Ga-H bond formation. As a result, the fully occupied bonding $pi$ band in BaGaGe changes to a weakly dispersive band with Ge pz (lone pair) character in the hydride, which becomes located just below the Fermi level. The Ga-Ge bonds within a layered polyanion are slightly weakened by hydrogen incorporation. A rationale for this is given.