Merkel cell carcinoma (MCC) is a rare form of aggressive skin cancer mainly caused by Merkel cell polyomavirus (MCPyV). Most MCC tumors express MCPyV large T (LT) antigens and play an important role in the growth-promoting activities of oncoproteins. Truncated LT promotes tumorigenicity as well as host cell proliferation by activating the viral replication machinery, and inhibition of this protein in humans drastically lowers cellular growth linked to the corresponding cancer. Our study was designed with the aim of identifying small molecular-like natural antiviral candidates that are able to inhibit the proliferation of malignant tumors, especially those that are aggressive, by blocking the activity of viral LT protein. To identify potential compounds against the target protein, a computational drug design including molecular docking, ADME (absorption, distribution, metabolism, and excretion), toxicity, molecular dynamics (MD) simulation, and molecular mechanics generalized Born surface area (MM-GBSA) approaches were applied in this study. Initially, a total of 2190 phytochemicals isolated from 104 medicinal plants were screened using the molecular docking simulation method, resulting in the identification of the top five compounds having the highest binding energy, ranging between −6.5 and −7.6 kcal/mol. The effectiveness and safety of the selected compounds were evaluated based on ADME and toxicity features. A 250 ns MD simulation confirmed the stability of the selected compounds bind to the active site (AS) of the target protein. Additionally, MM-GBSA analysis was used to determine the high values of binding free energy (ΔG bind) of the compounds binding to the target protein. The five compounds identified by computational approaches, Paulownin (CID: 3084131), Actaealactone (CID: 11537736), Epigallocatechin 3-O-cinnamate (CID: 21629801), Cirsilineol (CID: 162464), and Lycoricidine (CID: 73065), can be used in therapy as lead compounds to combat MCPyV-related cancer. However, further wet laboratory investigations are required to evaluate the activity of the drugs against the virus.