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Preliminary studies have shown the superiority of convolutional neural networks (CNNs) compared to other network architectures for determining the surface quality of friction stir welds. In this paper, CNNs were employed to detect cavities inside friction stir welds by evaluating inline measured process data. The aim was to determine whether CNNs are suitable for identifying surface defects exclusively, or if the approach is transferable to internal weld defects. For this purpose, 120 welds were produced and examined by ultrasonic testing, which was the basis for labeling the data as “good” or “defective.” Different types of artificial neural network were tested for predicting the placement of the welds into the defined classes. It was found that the way of labeling the data is significant for the accuracy achievable. When the complete welds were uniformly labeled as “good” or “defective,” an accuracy of 98.5% was achieved by a CNN, which was a significant improvement compared to the state of the art. When the welds were labeled segment-wise, an accuracy of 79.2% was obtained by using a CNN, showing that a segment-wise prediction of the cavities is also possible. The results confirm that CNNs are well suited for process monitoring in friction stir welding and their application enables the identification of various defect types.