In recent years, there has been a stronger demand for the weight reduction of components of various portable electronic devices. This work is motivated by the need to reduce the weight of a camera shutter module without much decreasing the torque generated by its magnetic circuit. Because the camera shutter speed is most significantly affected by the torque, the magnitude of the generated torque should also be considered in the design for the weight reduction. Thus, we formulate the design problem as a torque maximization problem under various mass constraints. Specifically, we propose to formulate it as a topology optimization problem of magnetic circuits and find optimal shapes of yokes (and magnets) in the circuits. For the maximization formulation, the objective function is chosen as the average of clockwise and counterclockwise torques over a whole range of rotation angles of a magnet corresponding to the shutter opening angle. Limits on the mass of the yoke and magnet in a magnetic circuit are imposed as constraints. The torque generated by a magnetic circuit is calculated by the modified Maxwell stress tensor method. A series of mass constraint ratios is considered to investigate the effects of the mass usage on the magnitude of torque generated by optimized circuits. The region occupied by the yoke (and the magnet) is designated as a design domain, while coils are assumed to belong to a non-design domain. By demonstrating that the optimized magnetic circuits outperform a nominal circuit, tile use of the average torque as an objective function including a corresponding treatment of a rotating magnet proposed in this work is shown to be effective for the topology optimization of magnetic circuits in a camera shutter module.