Noroviruses are a leading cause of gastroenteritis worldwide, yet the molecular mechanisms of how host antiviral factors restrict norovirus infection are poorly understood. Here, we present a CRISPR activation screen that identifies mouse genes which inhibit murine norovirus (MNV) replication. Detailed analysis of the major hit Trim7 demonstrates a potent inhibition of the early stages of MNV replication. Leveraging in vitro evolution, we identified MNV mutants that escape Trim7 restriction by altering the cleavage of the viral NS6-7 polyprotein precursor. NS6, but not the NS6-7 precursor, directly binds the substrate-binding domain of Trim7. Surprisingly, the selective polyprotein processing that enables Trim7 evasion inflicts a significant evolutionary burden, as viruses with decreased NS6-7 cleavage are strongly attenuated in viral replication and pathogenesis. Our data provide an unappreciated mechanism of viral evasion of cellular antiviral factors through selective polyprotein processing and highlight the evolutionary tradeoffs in acquiring resistance to host restriction factors. IMPORTANCE To maximize a limited genetic capacity, viruses encode polyproteins that can be subsequently separated into individual components by viral proteases. While classically viewed as a means of economy, recent findings have indicated that polyprotein processing can spatially and temporally coordinate the distinct phases of the viral life cycle. Here, we present a function for alternative polyprotein processing centered on immune defense. We discovered that selective polyprotein processing of the murine norovirus polyprotein shields MNV from restriction by the host antiviral protein Trim7. Trim7 can bind the viral protein NS6 but not the viral precursor protein NS6-7. Our findings provide insight into the evolutionary pressures that define patterns of viral polyprotein processing and uncover a trade-off between viral replication and immune evasion.