A fluid dispenser device including a dispenser head, a piston and an outlet valve. The dispenser head has a body defining a fluid expulsion channel terminated by a dispenser orifice, a rigid insert disposed in the channel, and a shutter element disposed in the channel and displaceable between a closed position and an open position. The shutter element is urged at rest towards its closed position and automatically displaced towards its open position while fluid is dispensed, returning automatically to its closed position. The shutter element forms a single piece with the rigid insert. The rigid insert forms or is secured to the outlet valve and is mechanically displaceable towards its actuated position while the fluid is being expelled, and being automatically returned to its rest position once the fluid has been expelled.