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Domain generalization typically requires data from multiple source domains for model learning. However, such strong assumption may not always hold in practice, especially in medical field where the data sharing is highly concerned and sometimes prohibitive due to privacy issue. This paper studies the important yet challenging single domain generalization problem, in which a model is learned under the worst-case scenario with only one source domain to directly generalize to different unseen target domains. We present a novel approach to address this problem in medical image segmentation, which extracts and integrates the semantic shape prior information of segmentation that are invariant across domains and can be well-captured even from single domain data to facilitate segmentation under distribution shifts. Besides, a test-time adaptation strategy with dual-consistency regularization is further devised to promote dynamic incorporation of these shape priors under each unseen domain to improve model generalizability. Extensive experiments on two medical image segmentation tasks demonstrate the consistent improvements of our method across various unseen domains, as well as its superiority over state-of-the-art approaches in addressing domain generalization under the worst-case scenario.