The modular matrix converter (MMC) integrates a multi-winding transformer with a three-phase-to-single-phase matrix converter for each phase, making it suitable for high-power, high-voltage applications. Predictive control is an advanced control technique widely applied to power converters due to its numerous advantages, including fast dynamic response, the elimination of the need for proportional gain, and straightforward implementation. This study proposes a model predictive control (MPC) strategy to regulate load currents, reactive power, and common-mode voltage in a three-phase modular matrix converter. The proposed MPC algorithm selects the optimal switching states from all valid options for the modular matrix converter to apply in the next control step. A cost function is then used to minimize the error between the predicted system variables and their reference values, ensuring that the best states are applied to the modular matrix converter. The proposed MPC technique effectively controls the load currents to follow the desired reference signals, maintains sinusoidal source current waveforms by regulating reactive power, and reduces the magnitude of the common-mode voltage. The performance of the proposed approach is demonstrated through simulation results obtained in the MATLAB/Simulink environment.