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Three-phase induction motors (IMs) are considered an essential part of electromechanical systems. Despite the fact that IMs operate efficiently under harsh environments, there are many cases where they indicate deterioration. A crucial type of fault that must be diagnosed early is stator winding faults as a consequence of short circuits. Motor current signature analysis is a promising method for the failure diagnosis of power systems. Wavelets are ideal for both time- and frequency-domain analyses of the electrical current of nonstationary signals. In this paper, the signal data are obtained from simulations of an induction motor for various stator winding fault conditions and one normal operating condition. Our main contribution is the presentation of a fault diagnostic system based on a hybrid discrete wavelet–CNN method. First, the time series of the currents are processed with discrete wavelet analysis. In this way, the harmonic frequencies of the faults are successfully captured, and features can be extracted that comprise valuable information. Next, the features are fed into a convolutional neural network (CNN) model that achieves competitive accuracy and needs significantly reduced training time. The motivations for integrating CNNs into wavelet analysis results for fault diagnosis are as follows: (1) the monitoring is automated, as no human operators are needed to examine the results; (2) deep learning algorithms have the potential to identify even more indistinguishable and complex faults than those that human eyes could.