  The cross sections of $\Upsilon $\ absorption by nucleons are calculated in
meson-baryon exchange model using an effective hadronic Lagrangian. Calculated
cross sections are found to peak near threshold followed by an increase which
tends to settle at large center of mass energy. Peak values are found in range
about 1.8 to 4 mb when cutoff parameter of monopole form factor is varied from
1.2 to 1.8 GeV. The results disagree with pQCD calculations but are consistent
with the effective value of the absorption cross section extracted from p-A
scattering data in E772 experiment at $\sqrt{s_{NN}}=39$ GeV. We use this data
value to find a best fit of the cutoff parameter which enables us provide
definite predictions for the values of $\Upsilon $ absorption cross sections by
nucleons for upcoming p-A scattering experiments at RHIC and LHC energies for
zero rapidity $b\bar{b}$ states. The results could be useful in studying the
effect of $\Upsilon $ absorption by nucleons at its production stage in
relativistic heavy-ion collision experiments. We also find that thermal
averaged values of total absorption cross sections are small enough to rule out
the effect of absorption of $\Upsilon $ by the comovers in the hadronic matter.
