Wapl induces cohesin dissociation from DNA throughout the mitotic cell cycle, modulating sister chromatid cohesion and higher-order chromatin structure. Cohesin complexes containing meiosis-specific kleisin subunits govern most aspects of meiotic chromosome function, but whether Wapl regulates these complexes remains unknown. We show that during C. elegans oogenesis WAPL-1 antagonizes binding of cohesin containing COH-3/4 kleisins, but not REC-8, demonstrating that sensitivity to WAPL-1 is dictated by kleisin identity. By restricting the amount of chromosome-associated COH-3/4 cohesin, WAPL-1 controls chromosome structure throughout meiotic prophase. In the absence of REC-8, WAPL-1 inhibits COH-3/4-mediated cohesion, which requires crossover-fated events formed during meiotic recombination. Thus, WAPL-1 promotes functional specialization of meiotic cohesin: WAPL-1-sensitive COH-3/4 complexes modulate higher-order chromosome structure, while WAPL-1-refractory REC-8 complexes provide stable cohesion. Surprisingly, a WAPL-1-independent mechanism removes cohesin before metaphase I. Our studies provide insight into how meiosis-specific cohesin complexes are regulated to ensure formation of euploid gametes.