In this paper we propose a novel approach in designing Robust Model Predictive Controllers (abbr. MPC) for systems with a Prescribed Performance in the states. In particular, general continuous-time nonlinear systems which are constrained in the states by prescribed performance functions and are affected by bounded, persistent, additive disturbances, are considered in this paper. With the proposed approach the constrained plant can be transformed into an unconstrained one, thus the optimization problem of the MPC becomes less complex, the computational burden is significantly reduced and the closed-loop system is proven to be Input-to-State Stable with respect to disturbances, while the inputs and states strictly remain in the predefined sets. The efficacy of the theoretic results is depicted by an academic simulation example and through comparison results.