Generalizing to out-of-distribution (OOD) data is a challenging task for existing deep learning approaches. This problem largely comes from the common but often incorrect assumption of statistical learning algorithms that the source and target data come from the same i.i.d. distribution. To tackle the limited variability of domains available during training, as well as domain shifts at test time, numerous approaches for domain generalization have focused on generating samples from new domains. Recent studies on this topic suggest that feature statistics from instances of different domains can be mixed to simulate synthesized images from a novel domain. While this simple idea achieves state-of-art results on various domain generalization benchmarks, it ignores structural information which is key to transferring knowledge across different domains. In this paper, we leverage the ability of humans to recognize objects using solely their structural information (prominent region contours) to design a Structural-Aware Feature Stylization method for domain generalization. Our method improves feature stylization based on mixing instance statistics by enforcing structural consistency across the different style-augmented samples. This is achieved via a multi-task learning model which classifies original and augmented images while also reconstructing their edges in a secondary task. The edge reconstruction task helps the network preserve image structure during feature stylization, while also acting as a regularizer for the classification task. Through quantitative comparisons, we verify the effectiveness of our method upon existing state-of-the-art methods on PACS, VLCS, OfficeHome, DomainNet and Digits-DG. The implementation is available at this repository.