This work presents a modified model predictive control (MPC) with open-circuit fault-detection and fault-tolerance capabilities for grid-connected multilevel inverters. The proposed self-healing model predictive control (SMPC) approximates the error in the inverter output voltage, and executes a diagnostic algorithm if this error exceeds a pre-defined tolerance. This diagnostic algorithm determines the switch with an open-circuit failure in a duration less than one fundamental period. After an open-circuit failure is detected, the controller will reduce the set of permissible control actions, allowing the inverter to retain healthy operation. Unlike the existing methods, the proposed SMPC combines fault-detection techniques with the direct application for corrective actions for fast fault clearness. The theoretical analysis and case studies verify the functionality of the proposed self-healing MPC scheme for a grid-tied seven-level cascaded multilevel inverter (CMI).