Deubiquitylases (DUBs) play a pivotal role in cell signalling and are often regulated by homo- or hetero-interactions within protein complexes. The BRCC36 isopeptidase complex (BRISC) regulates inflammatory signalling by selectively cleaving K63-linked polyubiquitin chains on Type I interferon receptors (IFNAR1/2). BRCC36 is a Zn2+-dependent JAMM/MPN DUB and a challenging target for selective inhibitors. We identified first-in-class DUB inhibitors that act as BRISC molecular glues (BLUEs). BLUEs inhibit DUB activity by stabilising a BRISC dimer consisting of 16 subunits. The BRISC dimer is an autoinhibited conformation, whereby the active sites and binding sites for the recruiting subunit SHMT2 are blocked. This unique mode of action leads to highly selective compounds for BRISC over related complexes with the same catalytic subunit, splice variants and other JAMM/MPN DUBs. Structure-guided inhibitor-insensitive BRISC mutants confirm BLUEs on-target activity in cells by lowering immune signalling intensity and duration, and by accelerating IFNAR1 degradation. We demonstrate a route to develop selective inhibitors through stabilising interactions with molecular glues and identify a new class of molecules for lowering inflammation in interferon-mediated conditions and autoimmune disease.