A ballast planing machine includes a machine frame supported by undercarriages for movement in an operating direction along a track and comprised of a leading carrier frame which supports a vertically adjustable ballast plow arrangement and a further carrier frame which is linked to the leading carrier frame and supports an operator's cabin and a vertically adjustable, rotary sweeping broom. Mounted to the further carrier frame is also a negative pressure generator of a suction unit for removing excess ballast during movement of the machine frame in operating direction. The suction unit includes a suction tube which communicates with the negative pressure generator and extends in longitudinal direction beyond the machine frame to terminate in a suction nozzle which projects beyond the rearward end of the machine frame. The suction nozzle is operatively connected to a control unit which is installed in the operator's cabin and controls a movement of the suction nozzle between an idle non-operational position and an operational position.