The rapid spread of Zika virus (ZIKV) and its association with abnormal brain development constitute a global health emergency. Congenital ZIKV infection produces a range of mild to severe pathologies, including placental damage and microcephaly. However, the placenta’s role in viral transmission and the mechanisms of microcephaly have not been addressed in primary human tissues. Moreover, there is an urgent need for drugs that can prevent developmental defects following infection. Here, we identify the placental and brain cell populations most susceptible to ZIKV infection, provide evidence for a mechanism of viral entry, and show that a commonly used antibiotic protects cultured brain cells by inhibiting viral proliferation. In the early gestation placenta, the virus readily infected trophoblast subpopulations that are in direct contact with maternal blood and uterine cells, suggesting routes of ZIKV transmission to the embryo and fetus. In the brain, ZIKV preferentially infected neural stem cells, astrocytes, and microglia, whereas neurons were less susceptible to infection. These findings suggest mechanisms for microcephaly and other pathologic features of infants with congenital ZIKV infection that are not explained by neural stem cell infection alone, such as calcifications in the cortical plate and brain abnormalities caused by third trimester infection. Blocking a putative viral entry receptor, AXL, which is highly enriched in the infected placenta and brain cell types, reduced ZIKV infection of astrocytes in vitro. In a glial cell line, the macrolide antibiotic, azithromycin, inhibited viral proliferation and viral-induced cytopathic effects at clinically relevant concentrations. Our characterization of infection in primary human tissues clarifies the pathogenesis of congenital ZIKV infection and provides critical context for interpreting results from model systems. Further work on azithromycin and related compounds may yield additional therapeutic strategies to safely alleviate or prevent the most severe consequences of the epidemic.