Zika virus (ZIKV) infection during pregnancy can lead to fetal brain infection and developmental anomalies collectively known as congenital Zika syndrome (CZS). To define the molecular features underlying CZS in a relevant human cell model, we evaluate ZIKV infection in primary human fetal brain explants and human induced pluripotent stem cell-derived mixed neural cultures at single-cell resolution. We identify astrocytes as important innate immune sentinel cells detecting ZIKV and producing interferon-beta (IFN-β). In contrast, neural stem cells display impaired innate immunity and support high levels of viral replication. ZIKV infection of neurons suppresses differentiation and synaptic signaling gene networks and programs a molecular switch from neurogenesis to astrogliogenesis. We identify a universal ZIKV-driven cellular stress response linked to intrinsic apoptosis and regulated by IFN-β. These findings reveal innate immune signaling intersecting with ZIKV-driven perturbations in cellular function to influence CZS outcomes including neuron developmental dysfunction and apoptotic cell death.