Early detection of potential side effects (SE) is a critical and challenging task for drug discovery and patient care. In-vitro or in-vivo approach to detect potential SEs is not scalable for many drug candidates during the preclinical stage. Recent advances in explainable machine learning may facilitate detecting potential SEs of new drugs before market release and elucidating the critical mechanism of biological actions. Here, we leverage multi-modal interactions among molecules to develop a biologically informed graph-based SE prediction model, called HHAN-DSI. HHAN-DSI predicted frequent and even uncommon SEs of the unseen drug with higher or comparable accuracy against benchmark methods. When applying HHAN-DSI to the central nervous system, the organs with the largest number of SEs, the model revealed diverse psychiatric medications' previously unknown but probable SEs, together with the potential mechanisms of actions through a network of genes, biological functions, drugs, and SEs.