Bacteria and archaea possess adaptive immune systems that rely on small RNAs for defense against invasive genetic elements. CRISPR (clustered regularly interspaced short palindromic repeats) genomic loci are transcribed as long precursor RNAs, which must be enzymatically cleaved to generate mature CRISPR-derived RNAs (crRNAs) that serve as guides for foreign nucleic acid targeting and degradation. This processing occurs within the repetitive sequence and is catalyzed by a dedicated Cas6 family member in many CRISPR systems. In Pseudomonas aeruginosa, crRNA biogenesis requires the endoribonuclease Csy4 (Cas6f), which binds and cleaves at the 3' side of a stable RNA stem-loop structure encoded by the CRISPR repeat. We show here that Csy4 recognizes its RNA substrate with an ~50 pM equilibrium dissociation constant, making it one of the highest-affinity protein:RNA interactions of this size reported to date. Tight binding is mediated exclusively by interactions upstream of the scissile phosphate that allow Csy4 to remain bound to its product and thereby sequester the crRNA for downstream targeting. Substrate specificity is achieved by RNA major groove contacts that are highly sensitive to helical geometry, as well as a strict preference for guanosine adjacent to the scissile phosphate in the active site. Collectively, our data highlight diverse modes of substrate recognition employed by Csy4 to enable accurate selection of CRISPR transcripts while avoiding spurious, off-target RNA binding and cleavage.