Monkeypox virus is the causative agent of monkeypox disease, belonging to an orthopoxvirus genus, with a disease pattern similar to that of smallpox. The number of monkeypox cases have robustly increased recently in several countries around the world, potentially causing an international threat. Therefore, serious measures are indispensable to be taken to mitigate the spread of the disease and hence, under these circumstances, vaccination is the best choice to neutralize the monkeypox virus. In the current study, we used immunoinformatic approaches to target the L1R, B5R, and A33R proteins of the monkeypox virus to screen for immunogenic cytotoxic T-lymphocyte (CTL), helper T-lymphocyte (HTL), and B-cell epitopes to construct multiepitope subunit vaccines. Various online tools predicted the best epitope from immunogenic targets (L1R, B5R, and A33R) of monkeypox virus. The predicted epitopes were joined together by different linkers and subjected to 3D structure prediction. Molecular dynamics simulation analysis confirmed the proper folding of the modeled proteins. The strong binding of the constructed vaccines with human TLR-2 was verified by the molecular docking and determination of dissociation constant values. The GC content and codon adaptation index (CAI) values confirmed the high expression of the constructed vaccines in the pET-28a (+) expression vector. The immune response simulation data delineated that the injected vaccines robustly activated the immune system, triggering the production of high titers of IgG and IgM antibodies. In conclusion, this study provided a solid base of concept to develop dynamic and effective vaccines that contain several monkeypox virus-derived highly antigenic and nonallergenic peptides to control the current pandemic of monkeypox virus.