Zika virus (ZIKV) infection has a profound impact on the fetal nervous system. The postnatal period is also a time of rapid brain growth, and it is important to understand the potential neurobehavioral consequences of ZIKV infection during infancy. Here we show that postnatal ZIKV infection in a rhesus macaque model resulted in long-term behavioral, motor, and cognitive changes, including increased emotional reactivity, decreased social contact, loss of balance, and deficits in visual recognition memory at one year of age. Structural and functional MRI showed that ZIKV-infected infant rhesus macaques had persistent enlargement of lateral ventricles, smaller volumes and altered functional connectivity between brain areas important for socioemotional behavior, cognitive, and motor function (e.g. amygdala, hippocampus, cerebellum). Neuropathological changes corresponded with neuroimaging results and were consistent with the behavioral and memory deficits. Overall, this study demonstrates that postnatal ZIKV infection in this model may have long-lasting neurodevelopmental consequences.