Efficiency, reliability, and durability play a key role in modern drive systems in line with the Industry 4.0 paradigm and the sustainability trend. To ensure this, highly efficient motors and appropriate systems must be deployed to monitor their condition and diagnose faults during the operation. For these reasons, in recent years, more and more research has been focused on developing new methods for fault diagnosis of permanent magnet synchronous motors (PMSMs). This paper proposes a novel hybrid method for the automatic detection and classification of PMSM stator winding faults based on combining the continuous wavelet transform (CWT) analysis of the negative sequence component of the stator phase currents with a convolutional neural network (CNN). CWT scalogram images are used as the inputs of the CNN-based interturn short circuits fault classifier model. Experimental tests were carried out to verify the effectiveness of the proposed approach under various motor operating conditions and at an incipient stage of fault propagation. In addition, the effects of the input image format, CNN structure, and training process parameters on model accuracy and classification effectiveness were investigated. The results of the experimental tests confirmed the high effectiveness of fault detection (99.4%) and classification (97.5%), as well as other important advantages of the developed method.