Mechanisms by which certain RNA viruses, such as hepatitis C virus, establish persistent infections and cause chronic disease are of fundamental importance in viral pathogenesis. Mammalian positive-stranded RNA viruses establishing persistence typically possess genome-scale ordered RNA secondary structure (GORS) in their genomes. Murine norovirus (MNV) persists in immunocompetent mice and provides an experimental model to functionally characterize GORS. Substitution mutants were constructed with coding sequences in NS3/4- and NS6/7-coding regions replaced with sequences with identical coding and (di-)nucleotide composition but disrupted RNA secondary structure (F1, F2, F1/F2 mutants). Mutants replicated with similar kinetics to wild-type (WT) MNV3 in RAW264.7 cells and primary macrophages, exhibited similar (highly restricted) induction and susceptibility to interferon-coupled cellular responses and equal replication fitness by serial passaging of co-cultures. In vivo, both WT and F1/F2 mutant viruses persistently infected mice, although F1, F2 and F1/F2 mutant viruses were rapidly eliminated 1–7 days post-inoculation in competition experiments with WT. F1/F2 mutants recovered from tissues at 9 months showed higher synonymous substitution rates than WT and nucleotide substitutions that potentially restored of RNA secondary structure. GORS plays no role in basic replication of MNV but potentially contributes to viral fitness and persistence in vivo.