Zika virus is an emerging mosquito‐borne pathogen that is associated with Guillain–Barré syndrome in adults and microcephaly and other neurological defects in newborns. Despite being declared an international emergency by the World Health Organization, comparatively little is known about its biology. Here, we investigate the strategies employed by the virus to suppress the host antiviral response. We observe that once established, Zika virus infection is impervious to interferon treatment suggesting that the virus deploys effective countermeasures to host cell defences. This is confirmed by experiments showing that Zika virus infection impairs the induction of type‐I interferon as well as downstream interferon‐stimulated genes. Multiple viral proteins affect these processes. Virus‐mediated degradation of STAT2 acts to reduce type‐I and type‐III interferon‐mediated signaling. Further, the NS5 of Zika virus binds to STAT2, and its expression is correlated with STAT2 degradation by the proteasome. Together, our findings provide key insights into how Zika virus blocks cellular defense systems. This in turn is important for understanding pathogenesis and may aid in designing antiviral therapies.