The previously reported magnetic long-range order has been revisited in the Zn-Mg-rare-earth systems by means of neutron diffraction, magnetic susceptibility and microstructural analysis. It was found that the long-range order is absent in icosahedral quasicrystals, where only short-range spin correlations develop even at the lowest temperatures. The long-range order was attributed to the (Zn x Mg 1 - x ) 5 -rare-earth crystalline phase, which was shown to be a contaminating phase in the previously used samples. The short-range spin correlations have been investigated in detail by single quasicrystal neutron scattering. A close relation has been suggested between the short-range correlations and the quasiperiodic structure.