In contrast to the DNA-based viruses in prokaryotes, the emergence of eukaryotes provided the necessary compartmentalization and membranous environment for RNA viruses to flourish, creating the need for an RNA-targeting antiviral system. Present day eukaryotes employ at least two main defence strategies that emerged as a result of this viral shift, namely antiviral RNA interference and the interferon system. Here we demonstrate that Drosha and related RNase III ribonucleases from all three domains of life also elicit a unique RNA-targeting antiviral activity. Systemic evolution of ligands by exponential enrichment of this class of proteins illustrates the recognition of unbranched RNA stem loops. Biochemical analyses reveal that, in this context, Drosha functions as an antiviral clamp, conferring steric hindrance on the RNA-dependent RNA polymerases of diverse positive-stranded RNA viruses. We present evidence for cytoplasmic translocation of RNase III nucleases in response to virus in diverse eukaryotes including plants, arthropods, fish, and mammals. These data implicate RNase III recognition of viral RNA as an antiviral defence that is independent of, and possibly predates, other known eukaryotic antiviral systems.