The mechanisms underlying Zika virus (ZIKV)-related microcephaly and other neurodevelopment defects remain poorly understood. Here, we describe the derivation and characterization, including single-cell RNA-seq, of neocortical and spinal cord neuroepithelial stem (NES) cells to model early human neurodevelopment and ZIKV-related neuropathogenesis. By analyzing human NES cells, organotypic fetal brain slices, and a ZIKV-infected micrencephalic brain, we show that ZIKV infects both neocortical and spinal NES cells as well as their fetal homolog, radial glial cells (RGCs), causing disrupted mitoses, supernumerary centrosomes, structural disorganization, and cell death. ZIKV infection of NES cells and RGCs causes centrosomal depletion and mitochondrial sequestration of phospho-TBK1 during mitosis. We also found that nucleoside analogs inhibit ZIKV replication in NES cells, protecting them from ZIKV-induced pTBK1 relocalization and cell death. We established a model system of human neural stem cells to reveal cellular and molecular mechanisms underlying neurodevelopmental defects associated with ZIKV infection and its potential treatment.