A cleaning device for cleaning an outer cylindrical surface of an impression cylinder of a rotary printing machine includes a cleaning cloth pressed against the outer cylindrical surface by a beam. The beam is pivotally mounted to engage the cleaning cloth with the outer cylindrical surface upon pressurization of a pneumatic cylinder. A spring pivotally returns the beam to disengage the cleaning cloth with the outer cylindrical surface upon depressurization of the pneumatic cylinder. To assure radial clearance between the cleaning device and the gripper fingers of the impression cylinder, the pneumatic cylinder is depressurized at a first angular position of the impression cylinder and the pneumatic cylinder is subsequently pressurized at a second angular position of the impression cylinder. The first and second angular positions of the impression cylinder correspond respectively to the cleaning device nearing the vicinity of the gripper fingers and the cleaning device leaving the vicinity of the gripper fingers. The cleaning device includes a cam roller that engages a cam plate attached to the impression cylinder to control the engagement of the cleaning device with the outer cylindrical surface upon the pressurization of the pneumatic cylinder.