Using density functional theory in conjunction with many-body perturbation theory, we theoretically investigated the electronic structures of monolayers germanane and silicane in an applied out-of-plane uniform electric field. Our results show that although the band structures of both monolayers are affected by the electric field, the band gap width cannot be reduced to zero even for high field-strengths. Moreover, excitons are shown to be robust under electric fields, so that Stark shifts for the fundamental exciton peak is only of the order of a few meV for fields of 1 V Å −1 . The electric field has also no significant effect on electron probability distribution, as the exciton dissociation into free electron–hole pairs is not observed even at high electric field strengths. Franz-Keldysh effect is also studied in monolayers germanane and silicane. We found that, due to the shielding effect, the external field is prevented to induce absorption in the spectral region below the gap and only above-gap oscillatory spectral features are allowed. One can benefit from such a characteristic where the absorption near the band edge is not altered by the presence of an electric field, especially since these materials have excitonic peaks in the visible range.