Viperin is a radical S-adenosylmethionine (SAM) enzyme that inhibits viral replication by converting cytidine triphosphate (CTP) into 3'-deoxy-3',4'-didehydro-CTP and by additional undefined mechanisms operating through its N- and C-terminal domains. Here, we describe crystal structures of viperin bound to a SAM analogue and CTP or uridine triphosphate (UTP) and report kinetic parameters for viperin-catalyzed reactions with CTP or UTP as substrates. Viperin orients the C4' hydrogen atom of CTP and UTP similarly for abstraction by a 5'-deoxyadenosyl radical, but the uracil moiety introduces unfavorable interactions that prevent tight binding of UTP. Consistently, kcat is similar for CTP and UTP whereas the Km for UTP is much greater. The structures also show that nucleotide binding results in ordering of the C-terminal tail and reveal that this region contains a P-loop that binds the γ-phosphate of the bound nucleotide. Collectively, the results explain the selectivity for CTP and reveal a structural role for the C-terminal tail in binding CTP and UTP.