Zika virus (ZIKV) is a flavivirus transmitted via mosquitoes and sex to cause congenital neurodevelopmental defects, including microcephaly. Inherited forms of microcephaly (MCPH) are associated with disrupted centrosome organization. Similarly, we found that ZIKV infection disrupted centrosome organization. ZIKV infection disrupted the organization of centrosomal proteins including CEP63, a MCPH-associated protein. The ZIKV nonstructural protein NS3 bound CEP63, and expression of NS3 was sufficient to alter centrosome architecture and CEP63 localization. Loss of CEP63 suppressed ZIKV-induced centrosome disorganization, indicating that ZIKV requires CEP63 to disrupt centrosome organization. ZIKV infection or CEP63 loss decreased the centrosomal localization and stability of TANK-binding kinase 1 (TBK1), a regulator of the innate immune response. ZIKV infection also increased the centrosomal accumulation of the CEP63 interactor DTX4, a ubiquitin ligase that degrades TBK1. Therefore, we propose that ZIKV disrupts CEP63 function to increase centrosomal DTX4 localization and destabilization of TBK1, thereby tempering the innate immune response.