Robotic agriculture and, in particular, the harvesting of vegetables and fruits, requires the development of novel effective gripping devices. In this paper, we propose a gripper design for harvesting tomatoes of the Pomodoro di Belmonte Calabro and Cuore di bue varieties, which are grown by farmers in the Calabria region of Italy. The gripper design is based on the use of a palm mechanism and soft elements that allow harvesting tomatoes without damaging them. A 3D model has been developed, the force-torque characteristics have been calculated, and a prototype of the gripper has been built. Experimental studies of the gripper for grasping tomato fruit have been carried out in laboratory conditions. The developed gripper can be used for other varieties of large tomatoes.