A device for closing a delivery head of a dispensing machine for delivering fluid products includes a stationary support, a drive shaft, which rotates with respect to the stationary support around a vertical axis, and can be moved with respect to the stationary support along the same vertical axis, a cup-shaped closing element carried at the distal end of an arm fixed to a lower end of the drive shaft, and a screw and nut mechanism which controls a translation of the closing element in the direction of the longitudinal axis and a rotation movement to the longitudinal axis using a single actuator.