Hepatitis E virus (HEV) is primarily a hepatotropic virus that is responsible for acute hepatitis E in the general population and for chronic hepatitis in immunocompromised individuals. In the absence of a globally accessible vaccine, pegylated interferon-α and ribavirin are the only antiviral agents available for the treatment of chronic patients. As viral RNA-dependent RNA polymerases (RdRps) are indispensable for RNA replication, they are considered potential drug targets. In this study, we screened some well-known RdRp inhibitor molecules, notably, favipiravir, sofosbuvir, remdesivir, filibuvir, and tegobuvir. Of these, monotherapy with favipiravir and sofosbuvir inhibited the RdRp activity with an IC50 value of 10.2 ± 4.9 and 5.2 ± 2.9 μM, respectively, compared to the reference drug ribavirin (3.5 ± 1.6 μM). Further investigation of the combination therapy showed a reduction in viral RNA copy numbers by approximately 90%. Therefore, favipiravir has an additive effect when used with sofosbuvir. Therefore, we propose that favipiravir is a promising anti-HEV drug that can be used in combination with sofosbuvir.