The growth mechanism of an icosahedral quasicrystal and solute partitioning in a Mg-rich Mg–Zn–Y alloy were investigated. It is found that the preferred growth directions of the icosahedral quasicrystalline phase (I-phase) are along 5-fold axes and the planes perpendicular to the 5-fold axes grow in a facet manner. Due to the local compositional change at the solid/liquid interface, the planar growth is gradually replaced by cellular growth. During the nucleation of the primary I-phase, on a microscale, the distribution of the Y element is changed and concentrated along 5-fold directions in the remaining liquid. If the cooling rate is relatively slow, there will be more Y element in the remaining liquid after the formation of the primary I-phase. It causes that (I-phase + α-Mg) eutectic structures form around the primary I-phase. Almost all the Y element is exhausted after this stage. Especially, under a relatively slow cooling rate, the solute partitioning occurs during the growth process of the primary I-phase, which leads to the microshrinkage cavity and crack defects at the edge of the primary I-phase.