A suction-cup pick-up assembly (4) has a tubular stem (6), which is connected to a pneumatic suction device and is engaged in a tubular support body (5) in a sliding manner, a suction cup (9), which is fixed to a free end of the tubular stem (6) and can be connected to the pneumatic suction device through a shutter (11), which is engaged in the tubular stem (6) in a sliding manner, and a detection device (14) to detect the axial position of the shutter (11) along the tubular support body (5); the detection device (14) having a reference element (15) mounted on the shutter (11) and at least one detector element (16, 17, 18) mounted on the tubular support body (5) in order to interact with the reference element (15) and detect the axial position of the shutter (11).