Optimal power dispatch is an optimization procedure useful to control microgrids, ensuring a safe, reliable, efficient, and cost-effective operation. An interesting way to improve this method is by incorporating strategies that consider the stochastic behavior of the systems to establish robust controllers in case of variations in power generation and power demand. This work proposes an approach based on model predictive control (MPC) for the optimal active and reactive power dispatch of isolated microgrids. For this purpose, two management strategies have been developed based on optimization models considering linear approximations of the power flow equations. The proposed algorithms optimize operating costs, schedule the charging and discharging of the storage units (SUs), perform voltage regulation, reduce active power losses, and guarantee the generation-demand balance. Validation is performed in a co-simulation scheme between Matlab and DIgSILENT on a modified version of the IEEE 13-bus test feeder, incorporating prediction models of renewable generation and power demand. The results show that the proposed strategies are robust in the presence of uncertainty, present short convergence times, convenient for real-time applications, and guarantee power balance with reduced generation costs.