Since stroke is the main cause of various cerebrovascular diseases, deep learning-based stroke lesion segmentation on magnetic resonance (MR) images has attracted considerable attention. However, the existing methods often neglect the domain shift among MR images collected from different sites, which has limited performance improvement. To address this problem, we intend to change style information without affecting high-level semantics via adaptively changing the low-frequency amplitude components of the Fourier transform so as to enhance model robustness to varying domains. Thus, we propose a novel FAN-Net, a U-Net--based segmentation network incorporated with a Fourier-based adaptive normalization (FAN) and a domain classifier with a gradient reversal layer. The FAN module is tailored for learning adaptive affine parameters for the amplitude components of different domains, which can dynamically normalize the style information of source images. Then, the domain classifier provides domain-agnostic knowledge to endow FAN with strong domain generalizability. The experimental results on the ATLAS dataset, which consists of MR images from 9 sites, show the superior performance of the proposed FAN-Net compared with baseline methods.