This note addresses the control of linear time-invariant plants in the presence of unknown, bounded disturbances when the output of the plant is only measured at sampling instants determined by a self-triggered strategy. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant. The proposed solution is a cascade interconnection of a state observer and a self-triggered state feedback controller. We focus our attention on state observers that are only updated at sampling times and that are input-to-state stable (ISS) with respect to disturbances. Due to the cascade structure of the closed-loop system and the fact that self-triggered control strategies presented in the literature are ISS with respect to observation errors and exogenous disturbances, we conclude that the closed-loop is rendered ISS with respect to exogenous disturbances.