Many vibration isolators, such as passive vehicle mounting devices, have an inflexible stiffness. This article presents the development of a smart material vibration isolator based on magnetorheological elastomer (MRE), which has adjustable stiffness to minimize unwanted vibrations. The objective of this research is to first create a design for the vibration isolator, and then simulate a magnetic circuit. The Finite Element Method Magnetics (FEMM) software was employed to simulate the effectiveness of the electromagnetic circuit in generating a magnetic field through the vibration isolator by employing MRE samples. Pure iron was chosen as the material for the housing of the vibration isolator test rig. To attain an optimal magnetic field, an inventive design of the magnetic circuit, including examination of the wire type, size, and coil turn number, along with the housing material of the test rig, was performed. The study analyzed the performance of the MRE vibration isolator concerning different current inputs in the coil. The results indicate that the stiffness value of the MRE-based isolator system can be more effectively modified by increasing the current inputs. Therefore, a larger current input leads to a greater change in stiffness.