An ab initio investigation of the electric-field-gradient-induced birefringence of H-2, N-2, C2H2, and CH4 is presented. All Linear and nonlinear optical properties contributing to the induced anisotropy of the refractive index are computed by means of coupled cluster singles and doubles response theory. For systems of cubic or icosahedral symmetry, the only nonvanishing contribution to the induced birefringence within the semiclassical approach is due to the frequency-dependent dipole-dipole-quadrupole and dipole-dipole-magnetic dipole hyperpolarizabilities. These hyperpolarizabilities are important for accurate experimental determinations of the molecular quadrupole moment from electric-field-gradient-induced birefringence measurements.