The paper deals with an optimization of a magnetic circuit of the field exciter designed to control magnetorheological fluid (MRF) in a hybrid soft–rigid jaw gripper. The case discussed includes sealing of the MRF inside a cushion made of thermoplastic polyurethane (TPU). The shear stress distributions in the MRF upon magnetic field excitation have been analyzed for various permanent magnet, yoke, and air gap dimensions. In the developed numerical model of the magnetic field exciter, the geometry of the considered domain was parameterized. As part of the simulation study, more than 4600 variants of the magnetic circuit were analyzed, for which the shear stress distribution in the MRF inside the cushion was determined. The numerical model has been implemented in the Ansys Electronics Desktop 2020 finite element method (FEM) package. Research was focused on finding dimensions of the magnetic circuit that ensure the desired distribution of the shear stress in the MRF inside the cushion. The undeformed and deformed by axial plunging of the pin cushions geometries have been analyzed. The evaluation criteria were the achievement of the highest possible value of the shear stress and the uniformity of its distribution in the given cross-sectional area of the MRF inside the cushion. The main objective of the analysis was to design the magnetic field exciter for application in the jaw pads of a gripper using MRF cushions. Through research, a suitable configuration tailored to the needs of the application was proposed.