We calculate light-cone distribution amplitudes for non-relativistic bound states, including radiative corrections from relativistic gluon exchange to first order in the strong coupling constant. Our results apply to hard exclusive reactions with non-relativistic bound states in the QCD factorization approach like, for instance, [B_c → eta_c l nu] or [e+ e- → J/psi eta_c]. They also serve as a toy model for light-cone distribution amplitudes of light mesons or heavy B and D mesons.