The ongoing SARS-CoV-2 pandemic continues to lead to high morbidity and mortality. During pregnancy, severe maternal and neonatal outcomes and placental pathological changes have been described. We evaluate SARS-CoV-2 infection at the maternal-fetal interface using precision-cut slices (PCSs) of human placenta. Remarkably, exposure of placenta PCSs to SARS-CoV-2 leads to a full replication cycle with infectious virus release. Moreover, the susceptibility of placental tissue to SARS-CoV-2 replication relates to the expression levels of ACE2. Viral proteins and/or viral RNA are detected in syncytiotrophoblasts, cytotrophoblasts, villous stroma, and possibly Hofbauer cells. While SARS-CoV-2 infection of placenta PCSs does not cause a detectable cytotoxicity or a pro-inflammatory cytokine response, an upregulation of one order of magnitude of interferon type III transcripts is measured. In conclusion, our data demonstrate the capacity of SARS-CoV-2 to infect and propagate in human placenta and constitute a basis for further investigation of SARS-CoV-2 biology at the maternal-fetal interface.