Sudden cardiac death (SCD) from arrhythmias is a leading cause of mortality. For patients at high SCD risk, prophylactic insertion of implantable cardioverter defibrillators (ICDs) reduces mortality. Current approaches to identify patients at risk for arrhythmia are, however, of low sensitivity and specificity, which results in a low rate of appropriate ICD therapy. Here, we develop a personalized approach to assess SCD risk in post-infarction patients based on cardiac imaging and computational modelling. We construct personalized three-dimensional computer models of post-infarction hearts from patients’ clinical magnetic resonance imaging data and assess the propensity of each model to develop arrhythmia. In a proof-of-concept retrospective study, the virtual heart test significantly outperformed several existing clinical metrics in predicting future arrhythmic events. The robust and non-invasive personalized virtual heart risk assessment may have the potential to prevent SCD and avoid unnecessary ICD implantations.