Author Summary Viruses rely on the host cell for replication and have evolved sophisticated strategies to manipulate and harness the cellular metabolic pathways and defense responses. A better knowledge of these viral strategies will provide new targets for antiviral therapies. The N-terminus of the large tegument proteins of herpesviruses encodes an ubiquitin and NEDD8-specific deconjugase, but the function of the enzyme during virus replication is largely unknown. Here we report that, endogenously expressed BPLF1, the homolog encoded by Epstein-Barr virus (EBV), promotes a dramatic decrease of NEDD8-conjugates and the accumulation of free NEDD8 in cells entering the productive virus cycle. BPLF1 exerts its deneddylase activity in the nucleus, which promotes the accumulation of cullin-RING ligase (CRL) substrates that are required for efficient virus replication. Targeting of the viral enzyme 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 to an unexpected role of the cellular response to danger signals triggered by EBV reactivation in promoting virus replication.