In the pursuit of developing a fault-tolerant architecture for battery management systems, rapid detection and isolation are pivotal functions. This study presents a method for detecting current sensor faults in an electric vehicle battery management system. Electric vehicle battery systems are exposed to harsh operating conditions, which increases the risk of failures in various onboard components. The proposed current sensor fault detection method incorporates a state estimator and a disturbance observer based on a nonlinear battery cell model for estimating unknown currents. The disturbance observer can estimate the engaged current even when the current measurement is unavailable, thereby allowing the detection of current sensor faults by analyzing the residual between the estimated and measured currents. Experimental results conducted on a single battery cell demonstrate the successful detection of current sensor faults using the proposed method. This sensor fault detection method plays a crucial role in determining the operation of the backup algorithm.