In many prokaryotes, type III clustered regularly interspaced short palindromic repeat (CRISPR)-CRISPR-associated (Cas) systems detect and degrade invasive genetic elements by an RNA-guided, RNA-targeting multisubunit interference complex. The CRISPR-associated protein Csm6 additionally contributes to interference by functioning as a standalone RNase that degrades invader RNA transcripts, but the mechanism linking invader sensing to Csm6 activity is not understood. Here we show that Csm6 proteins are activated through a second messenger generated by the type III interference complex. Upon target RNA binding by the interference complex, its Cas10 subunit converts ATP into a cyclic oligoadenylate product, which allosterically activates Csm6 by binding to its CRISPR-associated Rossmann fold (CARF) domain. CARF domain mutations that abolish allosteric activation inhibit Csm6 activity in vivo, and mutations in the Cas10 Palm domain phenocopy loss of Csm6. Together, these results point to an unprecedented mechanism for regulation of CRISPR interference that bears striking conceptual similarity to oligoadenylate signalling in mammalian innate immunity.