Lassa fever virus, a member of the family Arenaviridae, is a highly endemic category A pathogen that causes 300,000-500,000 infections per year in Western Africa. The arenaviral nucleoprotein NP has been implicated in suppression of the host innate immune system, but the mechanism by which this occurs has remained elusive. Here we present the crystal structure at 1.5 Å of the immunosuppressive C-terminal portion of Lassa virus NP and illustrate that, unexpectedly, its 3D fold closely mimics that of the DEDDh family of exonucleases. Accompanying biochemical experiments illustrate that NP indeed has a previously unknown, bona fide exonuclease activity, with strict specificity for double-stranded RNA substrates. We further demonstrate that this exonuclease activity is essential for the ability of NP to suppress translocation of IFN regulatory factor 3 and block activation of the innate immune system. Thus, the nucleoprotein is a viral exonuclease with anti-immune activity, and this work provides a unique opportunity to combat arenaviral infections.