Recently, magnetorheological elastomers have become interesting smart materials with many new designs for robotics. Various applications have been built with magnetorheological elastomers, such as vibration absorbers, actuators, or valves, showing that this material is promising for industry applications. The objective of this study is to demonstrate that magnetorheological elastomers supported by a permanent magnet can create a soft gripper suitable for handling small and delicate objects such as fruits or candies. The novel concept of the gripper is proposed, exploring the features of a magnetorheological elastomer and a permanent magnet. This gripper uses the energy of a permanent magnet to provide a self-closing gripping mechanism. At the same time, the use of flexible material—elastomer allows it to hold delicate objects of various shapes. The effect of wrapping magnetorheological elastomer around a permanent magnet, the design process, and the characteristics of a soft gripper are presented. The effectiveness of the soft gripper was validated in a series of experiments that involved lifting various objects.