In this note, a robust model predictive control scheme for constrained discrete-time nonlinear systems affected by bounded disturbances and state-dependent uncertainties is presented. In order to guarantee the robust satisfaction of the state constraints, restricted constraint sets are introduced in the optimization problem, by exploiting the state-dependent nature of the considered class of uncertainties. Moreover, unlike the nominal model predictive control algorithm, a stabilizing state constraint is imposed at the end of the control horizon in place of the usual terminal constraint posed at the end of the prediction horizon. The regional input-to-state stability of the closed-loop system is analyzed. A simulation example shows the effectiveness of the proposed approach.