Late-stage or post-market identification of adverse drug reactions (ADRs) is a significant public health issue and a source of major economic liability for drug development. Thus, reliable in silico screening of drug candidates for possible ADRs would be advantageous. In this work, we introduce a computational approach that predicts ADRs by combining the results of molecular docking and leverages known ADR information from DrugBank and SIDER. We employed a recently parallelized version of AutoDock Vina (VinaLC) to dock 906 small molecule drugs to a virtual panel of 409 DrugBank protein targets. L1-regularized logistic regression models were trained on the resulting docking scores of a 560 compound subset from the initial 906 compounds to predict 85 side effects, grouped into 10 ADR phenotype groups. Only 21% (87 out of 409) of the drug-protein binding features involve known targets of the drug subset, providing a significant probe of off-target effects. As a control, associations of this drug subset with the 555 annotated targets of these compounds, as reported in DrugBank, were used as features to train a separate group of models. The Vina off-target models and the DrugBank on-target models yielded comparable median area-under-the-receiver-operating-characteristic-curves (AUCs) during 10-fold cross-validation (0.60-0.69 and 0.61-0.74, respectively). Evidence was found in the PubMed literature to support several putative ADR-protein associations identified by our analysis. Among them, several associations between neoplasm-related ADRs and known tumor suppressor and tumor invasiveness marker proteins were found. A dual role for interstitial collagenase in both neoplasms and aneurysm formation was also identified. These associations all involve off-target proteins and could not have been found using available drug/on-target interaction data. This study illustrates a path forward to comprehensive ADR virtual screening that can potentially scale with increasing number of CPUs to tens of thousands of protein targets and millions of potential drug candidates.