We consider a novel mechanism for J / psi production in nuclear collisions arising due to the high density of gluons. The resulting J / psi production cross section is evaluated as a function of rapidity and centrality. We compute the nuclear modification factor and show that the rapidity distribution of the produced J / psi's is significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate that gluon saturation in the colliding nuclei is a significant source of J / psi suppression and can explain the experimentally observed rapidity and centrality dependencies of the effect.