New detailed MHD-shock model computations are carried out for "C-type" low-velocity shocks (LVSs) that propagate through the molecular interstellar medium. Unlike many other C-shock models that adopt a population of H-2 levels that is in thermal equilibrium (static limit) and a fixed ortho-H-2/para-H-2 ratio (OPR), the present one assumes a level population that is, along with the OPR, in a stationary state. This modification is necessary because the OPR of preshock gas is probably smaller than 3, as has been verified in H-2 observations of NGC 2024. Ortho-para interconversions occur mainly through collisions of H-2 with H+, H-3(+), and H. The densities of H+ and H-3(+) are generally low in C-shocks. These species convert only a small fraction of para-H-2 into ortho-H-2 during the passage of the shock. However, proton exchange reactions are the principal process for shock speeds u(s) less than or similar to 15 km s(-1). At higher shock speeds, the OPR attains its equilibrium quickly through reactive H-H-2 collisions, owing to higher kinetic temperatures and atomic hydrogen abundances reached in the shocked gas. Ortho-para interconversions induced through H-2 interaction with dust grains and due to H-2 formation on dust were found to be too slow in LVSs. A grid of models is calculated for preshock densities of n(H) = 10(2), 10(4), and 10(6) cm(-3) and shock speeds from u(s) = 10-30 km s(-1). It is demonstrated that the OPR attains 3 in regions of shocked gas only if u(s) greater than or similar to 20 km s(-1) for preshock densities less than or similar to 10(3) cm(-3), while u(s) greater than or similar to 25 km s(-1) is required for higher densities. The OPR remains less than 3 for shocks with smaller speeds and may not even deviate much from its initial value at the lowest shock speeds examined. We present H-2 line intensities assuming an OPRinitial of unity and 3. They are compared with those computed with models in which the level population is in thermal equilibrium.