This paper presents a novel cable-driven gripper with perception capabilities for autonomous harvesting of strawberries. Experiments show that the gripper allows for more accurate and faster picking of strawberries compared to existing systems. The gripper consists of four functional parts for sensing, picking, transmission, and storing. It has six fingers that open to form a closed space to swallow a target strawberry and push other surrounding berries away from the target. Equipped with three IR sensors, the gripper controls a manipulator arm to correct for positional error, and can thus pick strawberries that are not exactly localized by the vision algorithm, improving the robustness. Experiments show that the gripper is gentle on the berries as it merely cuts the stem and there is no physical interaction with the berries during the cutting process. We show that the gripper has close-to-perfect successful picking rate when addressing isolated strawberries. By including internal perception, we get high positional error tolerance, and avoid using slow, high-level closed-loop control. Moreover, the gripper can store several berries, which reduces the overall travel distance for the manipulator, and decreases the time needed to pick a single strawberry substantially. The experiments show that the gripper design decreased picking execution time noticeably compared to results found in literature.