  The leading order non-relativistic QCD result for the quarkonium-hadron
interaction cross section is derived by using the QCD factorization formula
combined with the Bethe-Salpeter amplitude for the heavy quark bound state. Our
result shows the equivalence of this approach with the operator product
expansion even for the bound state scattering to leading order in QCD. We also
apply the formula to the charmonium system and investigate the relativistic
correction coming from the phase space of the reaction. We find that although
$J/\psi$-gluon cross-section gets a large relativistic correction at higher
energies, the correction becomes small in the $J/\psi$-hadron cross section due
to the increase of the gluon distribution at smaller $x$ inside the hadron.
