RNA viruses infecting vertebrates differ fundamentally in their ability to establish persistent infections with markedly different patterns of transmission, disease mechanisms and evolutionary relationships with their hosts. Although interactions with host innate and adaptive responses are complex and persistence mechanisms likely multi-factorial, we previously observed associations between bioinformatically predicted RNA secondary formation in genomes of positive-stranded RNA viruses with their in vivo fitness and persistence. To analyse this interactions functionally, we transfected fibroblasts with non-replicating, non-translated RNA transcripts from RNA viral genomes with differing degrees of genome-scale ordered RNA structure (GORS). Single-stranded RNA transcripts induced interferon-β mediated though RIG-I and PKR activation, the latter associated with rapid induction of antiviral stress granules. A striking inverse correlation was observed between induction of both cellular responses with transcript RNA structure formation that was independent of both nucleotide composition and sequence length. The consistent inability of cells to recognize RNA transcripts possessing GORS extended to downstream differences from unstructured transcripts in expression of TNF-α, other interferon-stimulated genes and induction of apoptosis. This functional association provides novel insights into interactions between virus and host early after infection and provides evidence for a novel mechanism for evading intrinsic and innate immune responses.