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Model predictive control (MPC) has become increasingly popular among researchers for modular multilevel converters (MMCs) due to its ability to incorporate multiobjective control and provide superior dynamic response. However, it is computationally challenging to implement it on MMCs when the number of submodules is increased. This paper proposes a finite control set (FCS) model predictive control (MPC) with reduced computational complexity for modular multilevel converters (MMCs). To accomplish this goal, a reduced order data-driven model is obtained using sparse identification of nonlinear systems (SINDy) by incorporating the input terms in the load current and circulating current dynamics. As a result, the need to use the arm voltages or the submodule capacitor voltages dynamic equations as in the case of a conventional FCS-MPC is eliminated. To improve the output current total harmonic distortion (THD) and reduce the effect of higher switching frequencies caused by the FCS-MPC, an updated cost function is proposed. The effectiveness of the proposed technique is validated by simulation and experimental results.