Epstein-Barr virus (EBV), a known tumorigenic virus, is associated with various neuropathies, including multiple sclerosis (MS). However, there is no anti-EBV FDA-approved drug available in the market. Our study targeted EBV protein EBV nuclear antigen 1 (EBNA1), crucial in virus replication and expressed in all the stages of viral latencies. This dimeric protein binds to an 18 bp palindromic DNA sequence and initiates the process of viral replication. We chose phytochemicals and FDA-approved MS drugs based on literature survey followed by their evaluation efficacies as anti-EBNA1 molecules. Molecular docking revealed FDA drugs ozanimod, siponimod, teriflunomide, and phytochemicals; emodin; protoapigenone; and EGCG bound to EBNA1 with high affinities. ADMET and Lipinski's rule analysis of the phytochemicals predicted favorable druggability. We supported our assessments of pocket druggability with molecular dynamics simulations and binding affinity predictions by the molecular mechanics generalized Born surface area (MM/GBSA) method. Our results establish a stable binding for siponimod and ozanimod with EBNA1 mainly via van der Waals interactions. We identified hot spot residues like I481', K477', L582', and K586' in the binding of ligands. In particular, K477' at the amino terminal of EBNA1 is known to establish interaction with two bases at the major groove of the DNA. Siponimod bound to EBNA1 engaging K477', thus plausibly making it unavailable for DNA interaction. Computational alanine scanning further supported the significant roles of K477', I481', and K586' in the binding of ligands with EBNA1. Conclusively, the compounds showed promising results to be used against EBNA1.