The ongoing epidemic of Zika virus (ZIKV) illustrates the importance of flaviviruses as emerging human pathogens. All vector-borne flaviviruses studied thus far have to overcome type I interferon (IFN) to replicate and cause disease in vertebrates. The mechanism(s) by which ZIKV antagonizes IFN signaling is unknown. Here, we report that the nonstructural protein NS5 of ZIKV and other flaviviruses examined could suppress IFN signaling, but through different mechanisms. ZIKV NS5 expression resulted in proteasomal degradation of the IFN-regulated transcriptional activator STAT2 from humans, but not mice, which may explain the requirement for IFN deficiency to observe ZIKV-induced disease in mice. The mechanism of ZIKV NS5 resembles dengue virus (DENV) NS5 and not its closer relative, Spondweni virus (SPOV). However, unlike DENV, ZIKV did not require the E3 ubiquitin ligase UBR4 to induce STAT2 degradation. Hence, flavivirus NS5 proteins exhibit a remarkable functional convergence in IFN antagonism, albeit by virus-specific mechanisms.