The accurate prediction of drug responses remains a formidable challenge, particularly at the single-cell level and in clinical treatment contexts. Some studies employ transfer learning techniques to predict drug responses in individual cells and patients, but they require access to target-domain data during training, which is often unavailable or only obtainable in future. In this study, we propose a novel domain generalization framework, termed FourierDrug, to address this challenge. Given the extracted feature from expression profile, we performed Fourier transforms and then introduced an asymmetric attention constraint that would cluster drug-sensitive samples into a compact group while drives resistant samples dispersed in the frequency domain. Our empirical experiments demonstrate that our model effectively learns task-relevant features from diverse source domains, and achieves accurate predictions of drug response for unseen cancer type. When evaluated on single-cell and patient-level drug response prediction tasks, FourierDrug--trained solely on in vitro cell line data without access to target-domain data--consistently outperforms or, at least, matched the performance of current state-of-the-art methods. These findings underscore the potential of our method for real-world clinical applications.