The Modular Multilevel Matrix Converter (M3C) has been proposed as an appropriate alternative to driving high-power machines due to characteristics such as modularity, medium-voltage operation, high power quality, reliability. Nevertheless, the control of M3C is complicated, especially in variable-speed applications, because large voltage oscillations can be produced in the floating capacitors. Therefore, this paper presents a vector control system that allows decoupled regulation of the floating capacitors of the M3C, whereas Field Oriented Control (FOC) is applied to regulate an induction machine. The effectiveness of the proposed control system is validated through M3C simulation model composed of 63 power cells M3C driving a 1250 HP induction machine.