The invention relates to a gripper apparatus for a cannulation robot and for gripping a cannula having a cannula holder. The gripper apparatus comprises two gripper elements and a moving device. The two gripper elements can be moved relative to each other and work in concert to grip the cannula holder. The moving device is designed to move the two gripper elements relative to each other and at least one of the gripper elements relative to the cannula holder. The gripper apparatus can thereby be brought into a gripping state, in which at least one of the gripper elements is engaged with the cannula holder, by means of the moving device.