A dispenser of a product in powder from, composed of: a case delimiting a housing; a reservoir removably installed in the housing, the reservoir being adapted to contain the product in powder form and having a dispensing orifice; and a device for obturating the dispensing orifice. The device has a blocking member in the form of a shutter mounted to the reservoir for movement between a position for closing the dispensing orifice and a position for opening the dispensing orifice. The housing, the reservoir and the device are constructed to enable the reservoir to be installed in the housing by a vertical linear movement and to cause automatic movement of the shutter from the position for closing to the position for opening in response to the vertical linear movement of the reservoir into the housing.