Interferon-induced proteins with tetratricopeptide repeats (IFITs) are innate immune effector molecules that are thought to confer antiviral defence through disruption of protein-protein interactions in the host translation-initiation machinery. However, it was recently discovered that IFITs can directly recognize viral RNA bearing a 5'-triphosphate group (PPP-RNA), which is a molecular signature that distinguishes it from host RNA. Here we report crystal structures of human IFIT5, its complex with PPP-RNAs, and an amino-terminal fragment of IFIT1. The structures reveal a new helical domain that houses a positively charged cavity designed to specifically engage only single-stranded PPP-RNA, thus distinguishing it from the canonical cytosolic sensor of double-stranded viral PPP-RNA, retinoic acid-inducible gene I (RIG-I, also known as DDX58). Mutational analysis, proteolysis and gel-shift assays reveal that PPP-RNA is bound in a non-sequence-specific manner and requires a 5'-overhang of approximately three nucleotides. Abrogation of PPP-RNA binding in IFIT1 and IFIT5 was found to cause a defect in the antiviral response by human embryonic kidney cells. These results demonstrate the mechanism by which IFIT proteins selectively recognize viral RNA, and lend insight into their downstream effector function.