This paper is concerned with cyber-physical attack detection problem in networked control systems subject to limited communication bandwidth. This constraint arises when an attack detection system is located at a remote site and so the required signals, measurement output and control signals, need to be transmitted over a digital communication channel. Therefore, data before being sent to the remote site must be encoded and converted from analog signals to digital signals by using quantizer. A quantizer maps the amount of information from a continuous space to a finite set which is compatible with the limited communication bandwidth. Considering the quantized measurement output, a detection algorithm by means of a set-membership filtering approach will be proposed. The algorithm consists of a prediction ellipsoid set and an estimation ellipsoid set updated with the quantized measurement output. The detection method depends on the existence of intersection between two sets computed by the filter. Simulation results for some possible physical and cyber attacks are provided to demonstrate the effectiveness of the proposed method.