Although the Zika virus (ZIKV) typically causes mild or no symptoms in adults, during the 2015−2016 outbreak, ZIKV infection in pregnancy resulted in a spectrum of diseases in infants, including birth defects and neurodevelopmental disorders identified in childhood. While intense clinical and basic science research has focused on the neurodevelopmental outcomes of prenatal ZIKV infection, less is known about the consequences of infection during early life. Considering the neurotropism of ZIKV and the rapidly-developing postnatal brain, it is important to understand how infection during infancy may disrupt neurodevelopment. This paper reviews the current knowledge regarding early postnatal ZIKV infection. Emerging clinical evidence supports the hypothesis that ZIKV infection during infancy can result in negative neurologic consequences. However, clinical data regarding postnatal ZIKV infection in children are limited; as such, animal models play an important role in understanding the potential complications of ZIKV infection related to the vulnerable developing brain. Preclinical data provide insight into the potential behavioral, cognitive, and motor domains that clinical studies should examine in pediatric populations exposed to ZIKV during infancy.