Theoretical confirmation of the experimentally observed phenomenon [Knudsen et al., Phys. Rev. Lett. 105, 213201 (2010)] of target structure-induced suppression of the ionization cross section for low-energy antiproton-molecular hydrogen collisions is given. To this end a novel time-dependent convergent close-coupling approach to the scattering problem that accounts for all possible orientations of the molecular target, has been developed. The approach is applied to study single ionization of molecular hydrogen on the wide energy range from 1 keV to 2 MeV with a particular emphasis on low energies. Results for the orientation-averaged total single ionization cross section are compared with available experimental data and good agreement is found at low (<20 keV) and high (>90 keV) energies. A minor discrepancy is found within a small energy gap near the maximum of the cross section.