In modern drive systems, the aim is to ensure their operational safety. Damage can occur not only to the components of the motor itself but also to the power electronic devices included in the frequency converter and the sensors in the measurement circuit. Critical damage to the electric drive that makes its further exploitation impossible can be prevented by using fault-tolerant control (FTC) algorithms. These algorithms are very often combined with diagnostic methods that assess the degree and type of damage. In this paper, a fault classification algorithm using an artificial neural network (ANN) is analysed for stator phase current sensors in AC motor drives. The authors confirm that the investigated classification algorithm works equally well on two different AC motors without the need for significant modifications, such as retraining the neural network when transferring the algorithm to another object. The method uses a stator current estimator to replace faulty sensor measurements in a vector control structure. The measured and estimated currents are then subjected to a classification process using a multilayer perceptron (MLP), which has the advantage of a small structure size compared to deep learning structures. The uniqueness of the method lies in the use of data in the training set that are not dependent on the parameters of a specific motor. Four types of current sensor faults were studied, namely total signal loss, gain error, offset, and signal saturation. Simulations were performed in a MATLAB/SIMULINK environment for drive systems with an induction motor (IM) and a permanent magnet synchronous motor (PMSM). The results show that the algorithm correctly evaluates the type of damage in more than 99.6% of cases regardless of the type of motor. Therefore, the results presented here may help to develop universal diagnostic methods that will work on a wide variety of motors.