Double-stranded RNA produced during viral replication and transcription activates both protein kinase R (PKR) and ribonuclease L (RNase L), which limits viral gene expression and replication through host shutoff of translation. In this study, we find that APOBEC3B forms a complex with PABPC1 to stimulate PKR and counterbalances the PKR-suppressing activity of ADAR1 in response to infection by many types of viruses. This leads to translational blockage and the formation of stress granules. Furthermore, we show that APOBEC3B localizes to stress granules through the interaction with PABPC1. APOBEC3B facilitates the formation of protein-RNA condensates with stress granule assembly factor (G3BP1) by protecting mRNA associated with stress granules from RNAse L-induced RNA cleavage during viral infection. These results not only reveal that APOBEC3B is a key regulator of different steps of the innate immune response throughout viral infection but also highlight an alternative mechanism by which APOBEC3B can impact virus replication without editing viral genomes.