This paper proposes a model predictive torque control scheme for induction machines. The approach utilizes an augmented Lagrangian method in combination with a tailored gradient algorithm to efficiently solve the optimal control problem. The problem formulation accounts for hexagonal voltage constraints as well as constraints on the phase currents and the DC link current. A tailored calculation scheme for energy-efficient current setpoints improves the performance and the stability of the approach. Experimental results with computation times of less than 100 μs on a dSPACE real-time platform prove the potential of the proposed torque control scheme.