During its most recent outbreak across the Americas, Zika virus (ZIKV) was surprisingly shown to cause fetal loss and congenital malformations in acutely and chronically infected pregnant women. However, understanding the underlying pathogenesis of ZIKV congenital disease has been hampered by a lack of relevant in vivo experimental models. Here we present a candidate New World monkey model of ZIKV infection in pregnant marmosets that faithfully recapitulates human disease. ZIKV inoculation at the human-equivalent of early gestation caused an asymptomatic seroconversion, induction of type I/II interferon-associated genes and proinflammatory cytokines, and persistent viremia and viruria. Spontaneous pregnancy loss was observed 16-18 days post-infection, with extensive active placental viral replication and fetal neurocellular disorganization similar to that seen in humans. These findings underscore the key role of the placenta as a conduit for fetal infection, and demonstrate the utility of marmosets as a highly relevant model for studying congenital ZIKV disease and pregnancy loss.