This paper presents an active output feedback fault-tolerant model predictive control (MPC) scheme for systems with sensor faults. The proposed control scheme actively steers the system in order to prevent loss of observability caused by a sensor fault. To this end, the standard tracking objective of the MPC controller is augmented with an observability cost term which strongly penalizes unobservable state and input trajectories. A numerical example illustrates the use of the proposed approach on a target estimation and tracking control problem with faulty sensors.