According to the invention, there is provided a cylinder cleaning device for use with a cleaning fabric supply roll having a cleaning fabric wound thereon. The cleaning fabric is supplied from the supply roll and pressed against the outer surface of a cylinder to clean the outer surface of the cylinder. The device comprises a frame and a roll receiver mounted on the frame. The outer surface of the supply roll is engaged with and received by the receiver. The device further a comprises a roll stabilizer for stabilizing the supply roll on the receiver when the supply roll is rotated on the receiver to supply the cleaning fabric and have a diameter correspondingly decreasing.