A method is proposed for measuring electric quadrupole moments of atoms and molecules in excited states by observing electric field gradient induced birefringence (quadrupolar birefringence) in regions of absorption. The theory is based on the general treatment of quadrupolar birefringence of Buckingham and Longuet-Higgins . For electric dipole allowed transitions the effect is proportional to the transition probability and to the difference between the quadrupole moment of the excited state and of the ground state. For electric quadrupole allowed transitions the effect is more complicated and involves the transition quadrupole. Using Coulomb approximation and SCF matrix elements, quantitative estimates of quadrupolar birefringence for 2 P ← 2 S and 2 D ← 2 S transitions in vapours of atomic lithium and sodium are obtained. The magnitude of the effect in these cases is such that a measurement of quadrupole moments of low-lying 2 P states in sodium and lithium is feasible.