The suppression of the J/\ensuremath{\Psi} production is attributed to shadowing in the initial state parton distributions in nuclei due to multiquark cluster formation and to the dissociation of the final cc\ifmmode\bar\else\textasciimacron\fi{} state in the nuclear medium. The model agrees with the hadron-nucleus and nucleus-nucleus collision data and predicts enhancement of the effect at the Relativistic Heavy Ion Collider energies. Nuclear transparency at these energies is also considered and found to increase the suppression. \textcopyright{} 1996 The American Physical Society.