G3BP1 is an RNA binding protein that condenses untranslating messenger RNAs into stress granules (SGs). G3BP1 is inactivated by multiple viruses and is thought to antagonize viral replication by SG-enhanced antiviral signaling. Here, we show that neither G3BP1 nor SGs generally alter the activation of innate immune pathways. Instead, we show that the RNAs encoded by West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 are prone to G3BP1-dependent RNA condensation, which is enhanced by limiting translation initiation and correlates with the disruption of viral replication organelles and viral RNA replication. We show that these viruses counteract condensation of their RNA genomes by inhibiting the RNA condensing function of G3BP proteins, hijacking the RNA decondensing activity of eIF4A, and/or maintaining efficient translation. These findings argue that RNA condensation can function as an intrinsic antiviral mechanism, which explains why many viruses inactivate G3BP proteins and suggests that SGs may have arisen as a vestige of this antiviral mechanism.