Rift Valley fever virus (RVFV) is an emerging infectious pathogen that causes severe disease in humans and livestock and has the potential for global spread. There are currently no proven safe and effective treatment options for RVFV infection. Inhibition of RNA binding to RVFV nucleocapsid protein (N) represents an attractive antiviral therapeutic strategy because several essential steps in the RVFV replication cycle involve N binding to viral RNA. In this study, we demonstrate the therapeutic potential of the drug suramin by showing that it functions well as an inhibitor of RVFV replication at multiple stages in human cell culture. Suramin has been used previously to treat trypanosomiasis in Africa. We characterize the dynamic and cooperative nature of N-RNA binding interactions and the dissociation of high-molecular-mass ribonucleoprotein complexes using suramin, which we previously identified as an N-RNA binding inhibitor in a high-throughput screen.