We report the asymptotic behavior of the electron-atom Compton profile due to the intramolecular H-atom motion in H2. The experiment has been performed at a scattering angle of 135° and at incident electron energies from 1.0 to 2.2 keV, thus covering a momentum transfer (K) range from 15.8 to 23.5 a.u. It is shown that with the increase in K, the Compton profile changes in shape and becomes more symmetric. Furthermore, it is found that the experiment reaches the limit of sufficiently large K at an incident electron energy of 2.0 keV, where the plane-wave impulse approximation is applicable to directly relate the Compton profile to the momentum distribution of the H atom.