Zika virus (ZIKV) infection of neural progenitor cells (NPCs) in utero is associated with neurological disorders, such as microcephaly, but a detailed molecular understanding of ZIKV-induced pathogenesis is lacking. Here we show that in vitro ZIKV infection of human cells, including NPCs, causes disruption of the nonsense-mediated mRNA decay (NMD) pathway. NMD is a cellular mRNA surveillance mechanism that is required for normal brain size in mice. Using affinity purification-mass spectrometry, we identified multiple cellular NMD factors that bind to the viral capsid protein, including the central NMD regulator up-frameshift protein 1 (UPF1). Endogenous UPF1 interacted with the ZIKV capsid protein in coimmunoprecipitation experiments, and capsid expression posttranscriptionally downregulated UPF1 protein levels, a process that we confirmed occurs during ZIKV infection. Cellular fractionation studies show that the ZIKV capsid protein specifically targets nuclear UPF1 for degradation via the proteasome. A further decrease in UPF1 levels by RNAi significantly enhanced ZIKV infection in NPC cultures, consistent with a model in which NMD restricts ZIKV infection in the fetal brain. We propose that ZIKV, via the capsid protein, has evolved a strategy to lower UPF1 levels and dampen antiviral activities of NMD, which in turn contributes to neuropathology in vivo IMPORTANCE Zika virus (ZIKV) is a significant global health threat, as infection has been linked to serious neurological complications, including microcephaly. Using a human stem cell-derived neural progenitor model system, we find that a critical cellular quality control process called the nonsense-mediated mRNA decay (NMD) pathway is disrupted during ZIKV infection. Importantly, disruption of the NMD pathway is a known cause of microcephaly and other neurological disorders. We further identify an interaction between the capsid protein of ZIKV and up-frameshift protein 1 (UPF1), the master regulator of NMD, and show that ZIKV capsid targets UPF1 for degradation. Together, these results offer a new mechanism for how ZIKV infection can cause neuropathology in the developing brain.