Micronuclei are membrane-encapsulated nuclear aberrations that form following cell division errors. Micronuclear membrane collapse results in DNA damage and cGAS-STING activation. TREX1 inhibits cGAS activation by degrading micronuclear DNA. Aside from a dependency on ER-tethering, the mechanisms directing TREX1 activity at micronuclei are unknown. Here, we identify BAF as a key regulator of TREX1 activity at micronuclei. BAF accumulates on micronuclei following membrane collapse and recruits TREX1 in a mechanism that depends on BAF interactions with LEM-domain proteins. Unexpectedly, despite delayed recruitment, TREX1 exhibits enhanced micronuclear DNA degradation and functions independently of the ER in BAF-deficient cells. Mechanistically, high concentrations of BAF inhibit TREX1-mediated DNA degradation in vitro in a manner that depends on BAF DNA-binding ability. BAF similarly outcompetes cGAS for micronuclear DNA and suppresses cGAS activation at micronuclei. Thus, ER-tethering allows TREX1 to selectively penetrate a BAF-dependent protective barrier at ruptured micronuclei that limits innate immunity in chromosomally unstable cells.