The Japanese encephalitis virus (JEV) is a mosquito-borne flavivirus that primarily affects people in Asia and seriously threatens public health. Considering the rising occurrence rates and lack of targeted antiviral treatments, it is essential to comprehend and tackle obstacles related to JEV in order to lessen its influence on world health. This investigation explores compounds derived from marine brown algae (Phaeophyceae) as potential inhibitors of JEV RNA-dependent RNA polymerase (RdRp), a critical enzyme in the virus’s replication cycle. Employing the computational virtual screen approach, four compounds, i.e., CMNPD16749, CMNPD2606, CMNPD27817, and CMNPD23662, with favorable binding energies ranging from −15.7 Kcal/mol to −13.9 kcal/mol were identified. Subsequently, through molecular docking analysis, the interactions responsible for the binding stability between the target protein and hit molecules compared to the reference molecule Galidesvir were studied. Further, through extensive molecular dynamic (MD) simulation studies at 200 ns, it was confirmed that each docked complex showed acceptable dynamic stability compared to the reference molecule. These findings were further validated using MM/PBSA free binding energy calculations, PCA analysis and free energy landscape construction. These computational findings suggested that the brown algae-derived compounds may act as an antiviral drug against JEV infection and lay a crucial foundation for future experimental studies against JEV.