We have observed an electric-field-induced change in the dimensionality of excitons in superlattices, from three to quasi-two dimensions. The exciton binding energy of a (40 Å/(40 Å) GaAs/(GaAl)As superlattice, determined from low-temperature photocurrent experiments, increases more than 6 meV by the action of an electric field perpendicular to the superlattice layers. This sharp increase, from nearly the bulk value of GaAs at very low fields to the isolated-quantum-well value at high fields, is a direct consequence of the Stark localization of electrons and holes in superlattices.