Global optimization of the geometry of small Ni clusters interacting with benzene molecules yields equilibrium structures where the Ni atoms find themselves caged between the benzene molecules. This leads to quenching of the Ni magnetic moment in most of the complexes even though the structure of the caged Ni clusters remain relatively unchanged from their otherwise free gas phase geometry. The accuracy of these predictions, based on density functional theory with generalized gradient approximation for exchange and correlation, is established by the good agreement achieved between the calculated and available experimental dissociation energies and ionization potentials.