An effective robust fuzzy model predictive control (RFMPC) method for secondary voltage control in islanded microgrids (μGs) is presented here. In contrast to the existing techniques, which require a detailed model of μG and an ideal communication network between μG central controller and primary local controllers, RFMPC is synthesized for a non-linear model of the μG with various time delays, uncertainties, and bounded disturbances. The famous Takagi-Sugeno fuzzy approach is adopted to approximate the inherently non-linear model of μG by locally linear dynamics. The Lyapunov-Razumikhin functional method is exploited to deal with time delays. In this regard, sufficient conditions are provided in the form of linear matrix inequalities (LMIs). Then, a sequence of control laws corresponding to a set of terminal constraints is computed offline. Doing so, the online stage is reduced to solving a convex problem with LMI constraints considering the sequence of constraint sets obtained in the offline stage, thereby reducing the computational burden significantly. Robust positive invariance and input-to-state stability property concerning communication network deficiency are then speculated. The effectiveness of the proposed RFMPC is verified via a comprehensive suite of simulations in the MATLAB/SimPowerSystems environment.