In this article, a robust model predictive control strategy is developed for networked cyber-physical systems under false data injections. The main feature of the proposed scheme relies on the capability to mitigate undesired system behaviors due to external malicious actions. This is achieved by showing that set-membership conditions allow us to quickly detect data integrity anomalies and, as a consequence, to implement adequate countermeasures. The core of the resulting solution exploits receding horizon and set-theoretic control ideas so that the resilient nature of the virtual control moves is formally put in light. Simulations on a $B747-100/200$ aircraft model show effectiveness and merits of the proposed resilient control architecture.