Infection with Asian-lineage Zika virus (ZIKV) has been associated with Guillain-Barré syndrome and fetal abnormalities, but the underlying mechanisms remain poorly understood. Animal models of infection are thus urgently needed. Here we show that rhesus macaques are susceptible to infection by an Asian-lineage ZIKV closely related to strains currently circulating in the Americas. Following subcutaneous inoculation, ZIKV RNA is detected in plasma 1 day post infection (d.p.i.) in all animals (N=8, including 2 pregnant animals), and is also present in saliva, urine and cerebrospinal fluid. Non-pregnant and pregnant animals remain viremic for 21 days and for up to at least 57 days, respectively. Neutralizing antibodies are detected by 21 d.p.i. Rechallenge 10 weeks after the initial challenge results in no detectable virus replication, indicating protective immunity against homologous strains. Therefore, Asian-lineage ZIKV infection of rhesus macaques provides a relevant animal model for studying pathogenesis and evaluating potential interventions against human infection, including during pregnancy.