This work proposes an advanced control framework for the energy management of an islanded microgrid, using Model Predictive Control (MPC) methodology empowered with Artificial Intelligence (AI). In this hybrid approach, AI models substitute complex mathematical modelling of power assets necessary for the MPC method to operate. More specifically, Neural Network (NN) models predict the State of Charge (SOC) for each battery stack of the microgrid nodes on an hourly horizon. The predictions are then introduced to a Nonlinear MPC (NMPC) controller, substituting the process model. The efficiency of the proposed approach is compared to state of the art NMPC framework, developed for the optimal energy management of the microgrid. The simulations show that the proposed hybrid approach provides appropriate control actions for efficient energy balance in the microgrid with 6.5% average reduction of the transferred energy, compared to that of the implementation based on Mechanistic Mathematical models (MM). Indicative results are presented so as to demonstrate the capability of the proposed method to provide efficient control for optimal energy management.