Protein-Protein interactions (PPIs) are crucial in various biological processes and their study has significant implications for drug development and disease diagnosis. Existing deep learning methods for PPIs prediction, suffer from remarkable performance degradation under complex real-world scenarios due to various factors, e.g., label scarcity and domain shift. Among these factors, topological shortcut of PPIs is considerable and limits model to capture the pattern of protein-protein structure, which makes generalization terrible. In addition, huge data growth of PPIs challenges computing device. In this paper, we propose a label-aware hierarchical subgraph learning framework (laruGL-PPI) that can effectively infer PPIs while being both interpretable and generalizable. In laruGL-PPI, we not only model the inner-outer connection of PPIs as a hierarchical graph but explore the label dependencies by constructing a label graph. Importantly, edge-based subgraph sampling is adopted to effectively alleviate the problems as topological shortcut and high computing cost. Extensive experiments on PPI datasets of different scales with various evaluation settings demonstrate that laruGL-PPI outperforms state-of-the-art PPI prediction methods, particularly in testing of unseen proteins. In addition, our model can recognize crucial sites of proteins, such as surface sites for binding and active sites for catalysis.