Persistent virus infection continuously produces non-self nucleic acids that activate cell-intrinsic immune responses. However, the antiviral defense evolved as a transient, acute phase response and the effects of persistently ongoing stimulation onto cellular homeostasis are not well understood. To study the consequences of long-term innate immune activation, we expressed the NS5B polymerase of Hepatitis C virus (HCV), which in absence of viral genomes continuously produces immune-stimulatory RNAs. Surprisingly, within 3 weeks, NS5B expression declined and the innate immune response ceased. Proteomics and functional analyses indicated a reduced proliferation of those cells most strongly stimulated, which was independent of interferon signaling but required mitochondrial antiviral signaling protein (MAVS) and interferon regulatory factor 3 (IRF3). Depletion of MAVS or IRF3, or overexpression of the MAVS-inactivating HCV NS3/4A protease not only blocked interferon responses but also restored cell growth in NS5B expressing cells. However, pan-caspase inhibition could not rescue the NS5B-induced cytostasis. Our results underline an active counter selection of cells with prolonged innate immune activation, which likely constitutes a cellular strategy to prevent persistent virus infections.