Medical image segmentation remains a major challenge under domain shifts caused by device and acquisition heterogeneity. Although appearance features vary significantly across domains, anatomical shapes are largely consistent. However, existing methods insufficiently exploit such shape priors, which limits their generalization ability. To address this issue, we propose a Fourier Transform-based Shape-Constrained framework (FTSC) for domain-generalized medical image segmentation. Specifically, FTSC leverages the Fourier Transform to extract phase components that capture structural information, and integrates shape priors via a distributed shape extraction network supervised by surface loss. In addition, a gated fusion module is introduced to adaptively combine segmentation predictions with shape constraints. Additionally, a student shape extraction network is distilled for label-free inference. Experiments on two public datasets demonstrate that FTSC achieves competitive performance compared to state-of-the-art domain generalization methods.