Liquid flow significantly influences dendritic growth behavior. Previous studies have shown that under forced convection, flow directed toward the dendrite tip enhances thermal dendrite growth. In contrast, shrinkage flow directed toward the tip suppresses thermal dendrite growth, although the underlying mechanism remains unclear. It also remains uncertain whether this effect similarly influences solute dendrites. In this study, we incorporated a density field into a quantitative phase-field model and coupled it with the Lattice Boltzmann method to simulate liquid flow. We began by examining the density-coupling and flow effects to investigate how shrinkage flow influences solute dendrite growth. Our findings indicate that shrinkage flow increases the liquid composition ahead of the dendritic tip, thereby suppressing dendritic growth—a trend consistent with that observed in thermal dendrites. Our analysis further shows that although the density-coupling effect promotes dendritic growth, the inhibitory effect of shrinkage flow is stronger. Unlike forced convection, shrinkage flow not only facilitates advective transport of solute but also introduces a source term in the composition field at the interface due to density variations. This source term expels solute, increasing the liquid composition ahead of the tip. Its presence is the fundamental mechanism by which shrinkage flow suppresses dendritic growth and also explains the inhibitory effect of shrinkage flow on thermal dendrites.