COVID-19 patients often develop severe cardiovascular complications, but it remains unclear if these are caused directly by viral infection or are secondary to a systemic response. Here, we examine the cardiac tropism of SARS-CoV-2 in human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) and smooth muscle cells (hPSC-SMCs). We find that that SARS-CoV-2 selectively infects hPSC-CMs through the viral receptor ACE2, whereas in hPSC-SMCs there is minimal viral entry or replication. After entry into cardiomyocytes, SARS-CoV-2 is assembled in lysosome-like vesicles and egresses via bulk exocytosis. The viral transcripts become a large fraction of cellular mRNA while host gene expression shifts from oxidative to glycolytic metabolism and upregulates chromatin modification and RNA splicing pathways. Most importantly, viral infection of hPSC-CMs progressively impairs both their electrophysiological and contractile function, and causes widespread cell death. These data support the hypothesis that COVID-19-related cardiac symptoms can result from a direct cardiotoxic effect of SARS-CoV-2.