Melanoma differentiation-associated gene-5 (MDA5) detects viral double-stranded RNA in the cytoplasm. RNA binding induces MDA5 to activate the signalling adaptor MAVS through interactions between the caspase recruitment domains (CARDs) of the two proteins. The molecular mechanism of MDA5 signalling is not well understood. Here, we show that MDA5 cooperatively binds short RNA ligands as a dimer with a 16-18-basepair footprint. A crystal structure of the MDA5 helicase-insert domain demonstrates an evolutionary relationship with the archaeal Hef helicases. In X-ray solution structures, the CARDs in unliganded MDA5 are flexible, and RNA binds on one side of an asymmetric MDA5 dimer, bridging the two subunits. On longer RNA, full-length and CARD-deleted MDA5 constructs assemble into ATP-sensitive filaments. We propose a signalling model in which the CARDs on MDA5-RNA filaments nucleate the assembly of MAVS filaments with the same polymeric geometry.