Zika virus (ZIKV) causes microcephaly and disrupts neurogenesis. Dicer-mediated miRNA biogenesis is required for embryonic brain development and has been suggested to be disrupted upon ZIKV infection. Here we mapped the ZIKV-host interactome in neural stem cells (NSCs) and found that Dicer is specifically targeted by the capsid from ZIKV, but not other flaviviruses, to facilitate ZIKV infection. We identified a capsid mutant (H41R) that loses this interaction and does not suppress Dicer activity. Consistently, ZIKV-H41R is less virulent and does not inhibit neurogenesis in vitro or corticogenesis in utero. Epidemic ZIKV strains contain capsid mutations that increase Dicer binding affinity and enhance pathogenicity. ZIKV-infected NSCs show global dampening of miRNA production, including key miRNAs linked to neurogenesis, which is not observed after ZIKV-H41R infection. Together these findings show that capsid-dependent suppression of Dicer is a major determinant of ZIKV immune evasion and pathogenesis and may underlie ZIKV-related microcephaly.