Zika virus (ZIKV) infection has emerged as a global health threat and infection of pregnant women causes intrauterine growth restriction, spontaneous abortion and microcephaly in newborns. Here we show using biologically relevant cells of neural and placental origin that following ZIKV infection, there is attenuation of the cellular innate response characterised by reduced expression of IFN-β and associated interferon stimulated genes (ISGs). One such ISG is viperin that has well documented antiviral activity against a wide range of viruses. Expression of viperin in cultured cells resulted in significant impairment of ZIKV replication, while MEFs derived from CRISPR/Cas9 derived viperin^−/− mice replicated ZIKV to higher titers compared to their WT counterparts. These results suggest that ZIKV can attenuate ISG expression to avoid the cellular antiviral innate response, thus allowing the virus to replicate unchecked. Moreover, we have identified that the ISG viperin has significant anti-ZIKV activity. Further understanding of how ZIKV perturbs the ISG response and the molecular mechanisms utilised by viperin to suppress ZIKV replication will aid in our understanding of ZIKV biology, pathogenesis and possible design of novel antiviral strategies.