Antiviral responses are often accompanied by translation inhibition and formation of stress granules (SG) in infected cells. However, the triggers for these processes and their role during infection remain subjects of active investigation. Copy-back viral genomes (cbVGs) are the primary inducers of the Mitochondrial Antiviral Signaling (MAVS) pathway and antiviral immunity during Sendai Virus (SeV) and Respiratory Syncytial virus (RSV) infections. The relationship between cbVGs and cellular stress during viral infections is unknown. Here we show that SG form during infections containing high levels of cbVGs, and not during infections with low levels of cbVGs. Moreover, using RNA fluorescent in situ hybridization to differentiate accumulation of standard viral genomes from cbVGs at a single-cell level during infection, we show that SG form exclusively in cells that accumulate high levels of cbVGs. PKR activation is increased during high cbVG infections and, as expected, PKR is necessary to induce virus-induced SG. However, SG form independent of MAVS signaling, demonstrating that cbVGs induce antiviral immunity and SG formation through two independent mechanisms. Furthermore, we show that translation inhibition and SG formation do not affect the overall expression of interferon and interferon stimulated genes during infection, making the stress response dispensable for antiviral immunity. Using live-cell imaging, we show that SG formation is highly dynamic and correlates with a drastic reduction of viral protein expression even in cells infected for several days. Through analysis of active protein translation at a single cell level, we show that infected cells that form SG show inhibition of protein translation. Together, our data reveal a new cbVG-driven mechanism of viral interference where cbVGs induce PKR-mediated translation inhibition and SG formation leading to a reduction in viral protein expression without altering overall antiviral immunity.