In the modern induction motor (IM) drive system, the fault-tolerant control (FTC) solution is becoming more and more popular. This approach significantly increases the security of the system. To choose the best control strategy, fault detection (FD) and fault classification (FC) methods are required. Current sensors (CS) are one of the measuring devices that can be damaged, which in the case of the drive system with IM precludes the correct operation of vector control structures. Due to the need to ensure current feedback and the operation of flux estimators, it is necessary to immediately compensate for the detected damage and classify its type. In the case of the IM drives, there are individual suggestions regarding methods of classifying the type of CS damage during drive operation. This article proposes the use of the classical multilayer perceptron (MLP) neural network to implement the CS neural fault classifier. The online work of this classifier was coordinated with the active FTC structure, which contained an algorithm for the detection and compensation of failure of one of the two CSs used in the rotor field-oriented control (DRFOC) structure. This article describes this structure and the method of designing the neural fault classifier (NN-FC). The operation of the NN-FC was verified by simulation tests of the drive system with an integrated FTC strategy. These tests showed the high efficiency of the developed fault classifier operating in the post-fault mode after compensating the previously detected CS fault and ensuring uninterrupted operation of the drive system.