A novel, single shot, nondestructive scheme to measure the bunch length of submillimeter relativistic electron bunches using the electro-optical method is described. In this scheme, the birefringence induced by the electric field of the electrons converts the temporal characteristics of the bunch to a spatial intensity distribution of an optical pulse. Electric field characteristics, induced birefringence, and retardation are calculated for a few typical electron beam parameters and criteria limiting the resolution are established.