We report on J/ψ production from asymmetric Cu + Au heavy-ion collisions at sNN=200 GeV at the Relativistic Heavy Ion Collider at both forward (Cu-going direction) and backward (Au-going direction) rapidities. The nuclear modification of J/ψ yields in Cu + Au collisions in the Au-going direction is found to be comparable to that in Au + Au collisions when plotted as a function of the number of participating nucleons. In the Cu-going direction, J/ψ production shows a stronger suppression. This difference is comparable in magnitude and has the same sign as the difference expected from shadowing effects due to stronger low-x gluon suppression in the larger Au nucleus.