The tunable dynamic mechanical property of MRE (magnetorheological elastomers) is desirable for improving the performance of automotive vibration isolation systems. The influence of magneto-sensitive rubber mounts on the dynamic behavior of automotive vibration isolation systems was investigated. The fractional-order derivative operator was introduced into a nonlinear model to characterize the rheological properties and amplitude dependence of the magneto-sensitive rubber. Based on the nonlinear viscoelastic constitutive relationship of magnetorheological elastomers, a nonlinear fractional-order dynamic model was developed. This model incorporated the elastic foundation and the coupling effect between the vehicle and suspension to analyze an automotive powertrain mounting system. Using numerical simulations, the effects of nonlinear viscoelastic properties on dynamic behavior were evaluated under engine start-up and constant-speed driving conditions. The results indicate that the displacement response amplitudes of the powertrain and the vehicle body decrease with increasing the fractional order and the nonlinear coefficient. Therefore, the vibration isolation performance of automotive mounts can be effectively improved by adjusting the stiffness of vibration isolation systems, which can be achieved by enhancing the viscosity and the amplitude dependence of magneto-sensitive rubber.