This paper presents a novel robust Model Predictive Control (MPC) algorithm for nonlinear systems represented through quasi-Linear Parameter Varying (qLPV) models. The nominal MPC predictions are made considering a frozen scheduling parameter guess, which is computationally cheaper than nonlinear predictions, while zonotopes bound the disturbance propagation along the prediction. These sets are computed with respect to the bounds of the variation of scheduling parameters, offering reduced conservatism of the closed-loop dynamics and ensuring input-to-state stability and recursive feasibility properties. A DC-DC converter benchmark example is used to illustrate the advantages of the proposed method.