The molecular mechanism of many drug side-effects is unknown and difficult to predict. Previous methods for explaining side effects have focused on known drug targets and their pathways as primary candidates. However, low affinity binding to proteins that are not usually considered drug targets may also drive side-effects. In order to assess these alternative targets, we used the 3D structures of 563 essential human proteins systematically to predict binding to 216 drugs. We first benchmarked our affinity predictions with available experimental data. We then combined singular value decomposition and canonical component analysis (SVD-CCA) to predict side-effects based on these novel target profiles. Our method predicts side-effects with good accuracy (average AUC: 0.82 for side effects present in < 50% of drug labels). We note that side-effect frequency is the most important feature for prediction, and can confound efforts at elucidating mechanism; our method allows us to remove the contribution of frequency and isolate novel biological signals. In particular, our analysis produces 2768 triplet associations between 50 essential proteins, 99 drugs and 77 side-effects. We validated a subset of these associations using experimental assay data. Our focus on essential proteins allows us to find associations that would likely be missed if we used recognized drug targets. Our associations provide novel insights about the molecular mechanisms of drug side-effects.