Nucleoside analogs have broad clinical utility as antiviral drugs. Key to their systemic distribution and cellular entry are human nucleoside transporters. Here, we establish that the human concentrative nucleoside transporter 3 (CNT3) interacts with antiviral drugs used in the treatment of coronavirus infections. We report high-resolution single-particle cryo-electron microscopy structures of bovine CNT3 complexed with antiviral nucleosides N4-hydroxycytidine, PSI-6206, GS-441524 and ribavirin, all in inward-facing states. Notably, we found that the orally bioavailable antiviral molnupiravir arrests CNT3 in four distinct conformations, allowing us to capture cryo-electron microscopy structures of drug-loaded outward-facing and drug-loaded intermediate states. Our studies uncover the conformational trajectory of CNT3 during membrane transport of a nucleoside analog antiviral drug, yield new insights into the role of interactions between the transport and the scaffold domains in elevator-like domain movements during drug translocation, and provide insights into the design of nucleoside analog antiviral prodrugs with improved oral bioavailability.