The self-triggered stabilization and safety problems, solved in the literature for deterministic systems, are here generalized for the class of stochastic systems. The state equations are described by an Ito differential equation driven by a Wiener noise, where the input generically enters both in the deterministic dynamics and in those affected by the noise. This class of system is of particular interest since in practice various disturbances, not measurable and that can be modeled in this way, may affect the dynamics. The obtained self-triggered control is applied to a simple example to check its effectiveness.