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We propose Path-CNN, a method for the segmentation of centerlines of tubular structures by embedding convolutional neural networks (CNNs) into the progressive minimal path method. Minimal path methods are widely used for topology-aware centerline segmentation, but usually these methods rely on weak, hand-tuned image features. In contrast, CNNs use strong image features which are learned automatically from images. But CNNs usually do not take the topology of the results into account, and often require a large amount of annotations for training. We integrate CNNs into the minimal path method, so that both techniques benefit from each other: CNNs employ learned image features to improve the determination of minimal paths, while the minimal path method ensures the correct topology of the segmented centerlines, provides strong geometric priors to increase the performance of CNNs, and reduces the amount of annotations for the training of CNNs significantly. Our method has lower hardware requirements than many recent methods. Qualitative and quantitative comparison with other methods shows that Path-CNN achieves better performance, especially when dealing with tubular structures with complex shapes in challenging environments.