We report a theoretical treatment of the nuclear spin-dependent spatial parity nonconserving (NSD-PNC) electron-nuclear interaction effect in the diatomic homonuclear ortho-H2 molecule. The magnetic dipole transition between v=1 and v=0 vibrational sublevels of the ground 1 Sigma g+ state is examined. The orthohydrogen molecule is a unique molecular system where the parity nonconserving (PNC) nuclear spin-dependent interaction due to the neutral weak currents can be directly observed and the corresponding coupling constant can be extracted from the future experiments. The theoretical simulation shows that using the cavity-enhanced scheme in conjunction with the record achievement of the intracavity absorption spectroscopy, the experiment on the observation of the NSD-PNC effect due to the neutral weak current in ortho-H-2 looks feasible.