The Zika virus (ZIKV) epidemic is associated with fetal brain lesions and other serious birth defects classified as congenital ZIKV syndrome. Postnatal ZIKV infection in infants and children has been reported; however, data on brain anatomy, function, and behavioral outcomes following infection are absent. We show that postnatal ZIKV infection of infant rhesus macaques (RMs) results in persistent structural and functional alterations of the central nervous system compared to age-matched controls. We demonstrate ZIKV lymphoid tropism and neurotropism in infant RMs and histopathologic abnormalities in the peripheral and central nervous systems including inflammatory infiltrates, astrogliosis, and Wallerian degeneration. Structural and resting-state functional magnetic resonance imaging (MRI/rs-fMRI) show persistent enlargement of lateral ventricles, maturational changes in specific brain regions, and altered functional connectivity (FC) between brain areas involved in emotional behavior and arousal functions, including weakened amygdala-hippocampal connectivity in two of two ZIKV-infected infant RMs several months after clearance of ZIKV RNA from peripheral blood. ZIKV infection also results in distinct alterations in the species-typical emotional reactivity to acute stress, which were predicted by the weak amygdala-hippocampal FC. We demonstrate that postnatal ZIKV infection of infants in this model affects neurodevelopment, suggesting that long-term clinical monitoring of pediatric cases is warranted.