Epidemiological studies of the COVID-19 pandemic have revealed evidence of cardiac involvement and documented that myocardial injury and myocarditis are predictors of poor outcomes. Nonetheless, little is understood regarding SARS-CoV-2 tropism within the heart and whether cardiac complications result directly from myocardial infection. Here, we develop a human engineered heart tissue model and demonstrate that SARS-CoV-2 selectively infects cardiomyocytes. Viral infection is dependent on expression of angiotensin-I converting enzyme 2 (ACE2) and endosomal cysteine proteases, suggesting an endosomal mechanism of cell entry. After infection with SARS-CoV-2, engineered tissues display typical features of myocarditis, including cardiomyocyte cell death, impaired cardiac contractility, and innate immune cell activation. Consistent with these findings, autopsy tissue obtained from individuals with COVID-19 myocarditis demonstrated cardiomyocyte infection, cell death, and macrophage-predominate immune cell infiltrate. These findings establish human cardiomyocyte tropism for SARS-CoV-2 and provide an experimental platform for interrogating and mitigating cardiac complications of COVID-19.