Ferromagnetism is found in nanocrystalline Zn/ZnO core-shell structures prepared by sputtering pure Zn with subsequent oxidation. The saturation magnetization (M(S)) of the passivated ZnO shells increases with decrease in average particle size (d). The Curie temperature of the samples is above 400 degrees C. It is found that the ferromagnetism has a close relationship with point defects in ZnO shells. The maximum magnetization is estimated to be 28 emu cm(-3) (i.e. 0.14 mu(B) per unit cell) at 300 K, which is over three orders of magnitude larger than that of undoped ZnO nanoparticles or nanorods (10(-3)-10(-2) emu cm(-3)). More importantly, there is a scaling relation of M(s) alpha 1/d(n) (n = 5.20 +/- 0.20) for samples with d <or= 76 nm despite substantial differences in the particle size and shape. The results suggest that defects at the interface of the Zn/ZnO heterostructure make the main magnetic contributions.