The large tegument proteins of herpesviruses contain N-terminal cysteine proteases with potent ubiquitin and NEDD8-specific deconjugase activities, but the function of the enzymes during virus replication remains largely unknown. Using as model BPLF1, the homologue encoded by Epstein-Barr virus (EBV), we found that induction of the productive virus cycle does not affect the total level of ubiquitin-conjugation but is accompanied by a BPLF1-dependent decrease of NEDD8-adducts and accumulation of free NEDD8. Expression of BPLF1 promotes cullin degradation and the stabilization of cullin-RING ligases (CRLs) substrates in the nucleus, while cytoplasmic CRLs and their substrates are not affected. The inactivation of nuclear CRLs is reversed by the N-terminus of CAND1, which inhibits the binding of BPLF1 to cullins and prevents efficient viral DNA replication. Targeting of the deneddylase activity to the nucleus is dependent on processing of the catalytic N-terminus by caspase-1. Inhibition of caspase-1 severely impairs viral DNA synthesis and the release of infectious virus, pointing a previously unrecognized role of the cellular response to danger signals triggered by EBV reactivation in promoting virus replication.