We report a remarkable enhancement of the magnetic moments of excitons as a result of their motion. This surprising result, which we have observed in magneto-optical studies of three distinct zinc-blende semiconductors, GaAs, CdTe, and ZnSe, becomes significant as the kinetic energy of the exciton becomes comparable with its Rydberg energy and is attributed to motionally induced changes in the internal structure of the exciton. The enhancement of the magnetic moment as a function of the exciton translational wave vector can be represented by a universal equation.