Autonomous submerged dredging offers numerous benefits, such as reduced ship resistance and lower vacuum requirements for the dredge pumps. However, this method also presents new challenges, such as stability and buoyancy control, which must be addressed to minimize the energy requirements and ensure cost-effectiveness and sustainability. To achieve these goals, this paper proposes a Model Predictive Control (MPC) strategy to minimize control effort and energy requirements. Compared to traditional motion control methods such as proportional–integral–derivative (PID) control, MPC shows great promise in terms of energy efficiency and trajectory-tracking. The Autonomous Low Energy Replenishment Dredger (ALERD) is used as a case study to showcase the potential of the proposed control strategy. A time-domain simulation model is developed, and the ALERD is modeled as an underwater vehicle using a state-space representation. The classic PID control and the proposed MPC framework are compared in terms of trajectory-tracking, energy requirements, and robustness to modeling uncertainties, using sensitivity analysis. The results show that the proposed MPC control framework outperforms PID control in all aspects considered. Furthermore, a comparison between the energy requirements of the ALERD and a conventional dredger, for the same operational profile and hopper volume, indicates that autonomous submerged dredging can potentially decrease total energy requirements by 66%.