The present research deals with the dynamic characteristics and optimal design of the laminated composite CNT reinforced magnetorheological elastomer sandwich panel. The finite element (FE) formulation based on higher-order shear deformation theory (HSDT) is used to derive the governing equations of the composite sandwich panel. The conventional MR elastomer and CNT reinforced MR elastomer is fabricated and experimented to obtain the complex shear modulus with different magnetic fields using ASTM E756-05 standard test. The efficacy of the FE model is verified by correlating the results obtained using experimental investigations on the laminated composite MR elastomer and CNT reinforced MR elastomer sandwich panels. The dynamic characteristics and forced vibrations of the fully configured and various patterns of a partially configured CNT reinforced MR elastomer sandwich panels are examined. Finally, the optimum design of a partially configured CNT reinforced MR elastomer composite sandwich panel is developed using the FE model coupled with a genetic algorithm (GA) to enhance the natural frequencies, loss factors and suppress transverse displacements.