The secondary isotope shifts of six molecular hydrogen isotopologues (H-2, D-2, T-2, HD, HT, and DT) were measured using gas-phase nuclear magnetic resonance spectroscopy. It was found that these isotope shifts are in satisfying agreement with performed ab initio quantum chemistry computations. However, there is a small systematic discrepancy between results of experiments and computations, i.e., the magnitudes of computed shifts are approximately 10% larger than those obtained from the experiments. This indicates that computations performed using the Born Oppenheimer approximation are not sufficient for reproducing quantitatively the experimentally determined secondary isotope shifts of molecular hydrogen.