We systematically calculate the relativistic corrections to the polarization variables of prompt J/ψ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the S 3 [1] 1 and P 3 [1] J color-singlet and the S 3 [8] 1 , S 1 [8] 0 , and P 3 [8] J color-octet channels as well as the effects due to the mixing between the S 3 [8] 1 and D 3 [8] 1 channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the nonrelativistic-QCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, especially at small transverse momentum p T and large inelasticity z . The results obtained here and in our previous work on the unpolarized yield [Phys. Rev. D 90, 014045 (2014)] will help to render global analyses of prompt J/ψ production data more complete and hopefully to shed light on the J/ψ polarization puzzle.