The limited host tropism of numerous viruses causing disease in humans remains incompletely understood. One example is Zika virus (ZIKV), an RNA virus that has reemerged in recent years. Here, we demonstrate that ZIKV efficiently infects fibroblasts from humans, great apes, New and Old World monkeys, but not rodents. ZIKV infection in human—but not murine—cells impairs responses to agonists of the cGMP-AMP synthase/stimulator of IFN genes (cGAS/STING) signaling pathway, suggesting that viral mechanisms to evade antiviral defenses are less effective in rodent cells. Indeed, human, but not mouse, STING is subject to cleavage by proteases encoded by ZIKV, dengue virus, West Nile virus, and Japanese encephalitis virus, but not that of yellow fever virus. The protease cleavage site, located between positions 78/79 of human STING, is only partially conserved in nonhuman primates and rodents, rendering these orthologs resistant to degradation. Genetic disruption of STING increases the susceptibility of mouse—but not human—cells to ZIKV. Accordingly, expression of only mouse, not human, STING in murine STING knockout cells rescues the ZIKV suppression phenotype. STING-deficient mice, however, did not exhibit increased susceptibility, suggesting that other redundant antiviral pathways control ZIKV infection in vivo. Collectively, our data demonstrate that numerous RNA viruses evade cGAS/STING-dependent signaling and affirm the importance of this pathway in shaping the host range of ZIKV. Furthermore, our results explain—at least in part—the decreased permissivity of rodent cells to ZIKV, which could aid in the development of mice model with inheritable susceptibility to ZIKV and other flaviviruses.