Inferring drug-drug interactions (DDIs) is an essential step in drug development and drug administration. Most computational inference methods focus on modeling drug pharmacokinetics, aiming at interactions that result from a common metabolizing enzyme (CYP). Here, we introduce a novel prediction method, INDI (INferring Drug Interactions), allowing the inference of both pharmacokinetic, CYP-related DDIs (along with their associated CYPs) and pharmacodynamic, non-CYP associated ones. On cross validation, it obtains high specificity and sensitivity levels (AUC (area under the receiver-operating characteristic curve) ≥0.93). In application to the FDA adverse event reporting system, 53% of the drug events could potentially be connected to known (41%) or predicted (12%) DDIs. Additionally, INDI predicts the severity level of each DDI upon co-administration of the involved drugs, suggesting that severe interactions are abundant in the clinical practice. Examining regularly taken medications by hospitalized patients, 18% of the patients receive known or predicted severely interacting drugs and are hospitalized more frequently. Access to INDI and its predictions is provided via a web tool at http://www.cs.tau.ac.il/~bnet/software/INDI, facilitating the inference and exploration of drug interactions and providing important leads for physicians and pharmaceutical companies alike.