Distributed Model Predictive Control (DMPC) strategies require local controllers to share information among each other. Considering the importance of communication in such control strategies and the failures that may occur in the information-sharing network, this paper proposes to apply the distributed consensus algorithm as an information-exchange protocol for DMPC controllers. The advantage of the proposed protocol is twofold. First, it relaxes some communication assumptions usually made for DMPC controllers. Second, under some assumptions, it provides resilience against some communication failures such that the performance and the features of the implemented distributed controller are preserved. A case study of a microgrid system is provided as an example in which some simulations are carried out to illustrate the aforementioned advantages.