The Japanese encephalitis virus (JEV), a mosquito-borne flavivirus that causes viral encephalitis leading to neural damage, is a major threat in most Asian countries. The RNA-dependent RNA polymerase (RdRp) present in the viral genome is the key component for genome replication, making it an attractive target for antiviral drug development. In this study, the natural products from Echinacea angustifolia were retrieved for structure-based virtual screening against JEV–RdRp. The top six compounds (Echinacoside, Echinacin, Rutin, Cynaroside, Quercetagetin 7-glucoside, and Kaempferol-3-glucoside) were obtained based on the highest negative docking score, ADMET (absorption, distribution, metabolism, excretion, and toxicity), and molecular interaction. The computational analysis of these selected compounds against the co-crystallized ligands, i.e., ATP and GTP, were performed. Further, 100 ns molecular dynamic simulation and post-free binding energy calculation of all the selected compounds complexed with JEV–RdRP were performed to check the stability of the complexes. The obtained results showed considerable stability and intermolecular interaction with native ligand-binding site residues of JEV–RdRp. Hence, selected natural compounds are admissible inhibitors of JEV–RdRp protein and can be considered for future antiviral drug development studies.