A key mechanism of the current-induced magnetization dynamics is the spin torque from a spin polarized current (spin current), which couples to spatial gradient of magnetization. Recently, it was pointed out that a large spin current applied to a uniform ferromagnet leads to a spin-wave instability. In this paper, we show that such instability is absent in a state containing a domain wall. This may indicate that nucleation of magnetic domains occurs above a certain critical spin current. This scenario is supported by an explicit energy comparison between the uniformly magnetized state and the domain-wall state under spin current.