This paper addresses a sensor scheduling problem for a class of networked sensor systems whose sensors are spatially distributed and measurements are influenced by state dependent noise. Sensor scheduling is required to achieve power saving since each sensor operates with a battery power source. The scheduling problem is formulated as a model predictive control problem with single sensor measurement per time. It is assumed that all sensors have state dependent noise and have the same characteristics, which follows from the properties of networked sensor systems. We propose a fast and optimal sensor scheduling algorithm for a class of networked sensor systems. Computation time of the proposed algorithm is proportional to the number of sensors and does not depend on the prediction horizon. In addition, we provide a fast sensor scheduling algorithm for a general class of systems by using a linear approximation of the sensor model.