It is well-known that real-world changes constituting distribution shift adversely affect model performance. How to characterize those changes in an interpretable manner is poorly understood. Existing techniques to address this problem take the form of shift explanations that elucidate how to map samples from the original distribution toward the shifted one by reducing the disparity between these two distributions. However, these methods can introduce group irregularities, leading to explanations that are less feasible and robust. To address these issues, we propose Group-aware Shift Explanations (GSE), a method that produces interpretable explanations by leveraging worst-group optimization to rectify group irregularities. We demonstrate how GSE not only maintains group structures, such as demographic and hierarchical subpopulations, but also enhances feasibility and robustness in the resulting explanations in a wide range of tabular, language, and image settings.