In the framework of nonrelativistic quantum chromodynamics and the parton model, we estimate, in detail, the production cross section for polarized J/ψ from B meson decays. In order to contrast with data, we also take into account additional J/ψ production due to the decay of excited charmonium states. We calculate the helicity parameter α and, as an application, we study our results for the Fermilab Tevatron. This is in contrast with the earlier studies which were performed for prompt J/ψ production from pp̅ collisions. Our estimates are, for J/ψ from B decays, αJ/ψ=-0.04±0.06 and, for B decays to ψ′, αψ′=-0.03±0.07. These results have been evaluated in the J/ψ transverse momentum interval 10GeV<~kT<~30GeV. In the limit of the color singlet model, α shows a direct dependence on the Peterson parameter, thereby reflecting the dynamics of the b quark hadronization. With run II of the Tevatron, it is expected that the fits for α will improve by about a factor of 50, leading to better limits on the matrix elements.