Ultraluminous infrared galaxies (ULIRGs) show on average three times more emission in the rotational transitions of molecular hydrogen than expected based on their star formation rates. Using Spitzer archival data, we investigate the origin of excess warm H_2_ emission in 115 ULIRGs of the IRAS 1Jy sample. We find a strong correlation between H_2_ and [FeII] line luminosities, suggesting that excess H_2_ is produced in shocks propagating within neutral or partially ionized medium. This view is supported by the correlations between H_2_ and optical line ratios diagnostic of such shocks. The galaxies powered by star formation and those powered by active nuclei follow the same relationship between H_2_ and [FeII], with emission line width being the major difference between these classes (~500 and ~1000km/s, respectively). We conclude that excess H_2_ emission is produced as the supernovae and active nuclei drive outflows into the neutral interstellar medium of the ULIRGs. A weak positive correlation between H_2_ and the length of the tidal tails indicates that these outflows are more likely to be encountered in more advanced mergers, but there is no evidence for excess H_2_ produced as a result of the collision shocks during the final coalescence.