Concomitant administration of drugs can cause drug-drug interactions (DDIs). Some drug combinations are beneficial, but other ones may cause negative effects which are previously unrecorded. Previous works on DDI prediction usually rely on hand-engineered domain knowledge, which is laborious to obtain. In this work, we propose a novel model, Molecular Substructure-Aware Network (MSAN), to effectively predict potential DDIs from molecular structures of drug pairs. We adopt a Transformer-like substructure extraction module to acquire a fixed number of representative vectors that are associated with various substructure patterns of the drug molecule. Then, interaction strength between the two drugs' substructures will be captured by a similarity-based interaction module. We also perform a substructure dropping augmentation before graph encoding to alleviate overfitting. Experimental results from a real-world dataset reveal that our proposed model achieves the state-of-the-art performance. We also show that the predictions of our model are highly interpretable through a case study.