We present a linear stability analysis of a planar ice interface during unidirectional solidification of a hard-sphere colloidal suspension. We find that the interface can become unstable due to constitutional supercooling, yielding a new mechanism for pattern formation in colloidal systems. The interfacial stability is shown to depend strongly on the size and concentration of the particles. Increasing the particle radius tends to stabilize the interface, while increasing the concentration has a destabilizing effect. Additional effects that may influence the stability and morphology of such a system are described.