Infection by the Severe Acute Respiratory Syndrome-Coronavirus-2 (SARS-CoV-2) results in the novel coronavirus disease COVID-19, which has posed a serious threat globally. Infection of SARS-CoV-2 during pregnancy is associated with complications like preterm labor and premature rupture of membranes; a proportion of neonates born to the infected mothers are also positive for the virus. During pregnancy, the placental barrier protects the fetus from pathogens and ensures healthy development. However, whether or not SARS-CoV-2 can infect the placenta is unknown. Herein, utilizing single-cell RNA-seq data, we report that the SARS-CoV-2 binding receptor ACE2 and the S protein priming protease TMPRSS2 are co-expressed by a subset of syncytiotrophoblasts (STB) in the first trimester and extra villous trophoblasts (EVT) in the second trimester human placenta. The ACE2- and TMPRSS2-positive (ACE2+TMPRSS2+) placental subsets express mRNA for proteins involved in viral budding and replication. These cells also express mRNA for proteins that interact with SARS-CoV-2 structural and non-structural proteins in the host cells. We also discovered unique signatures of genes in ACE2+TMPRSS2+ STBs and EVTs. The ACE2+TMPRSS2+ STBs are highly differentiated cells and express genes involved mitochondrial metabolism and glucose transport. The second trimester ACE2+TMPRSS2+ EVTs are enriched for markers of endovascular trophoblasts. Further, both these subtypes abundantly expressed genes in Toll like receptor pathway, the second trimester EVTs (but not first trimester STBs) are also enriched for component of the JAK-STAT pathway that drive inflammation. To conclude, herein we uncovered the cellular targets for SARS-CoV-2 entry and show that these cells can potentially drive viremia in the developing human placenta. Our results provide a basic framework towards understanding the paraphernalia involved in SARS-CoV-2 infections in pregnancy.