A fluid dispenser device having a body (1), and a dispenser head (2) provided with an orifice (3) and that is axially movable relative to the body (1). The body receives a reservoir (10) containing fluid, the reservoir has a hollow tube (11) having a proximal axial opening (12) closed by a stopper (20) adapted to slide in the tube (11). The dispenser head (2) includes a hollow cannula (4) connected at one end to the dispenser orifice (3), and provided at its other end with a perforating tip (5) having an opening (6) for perforating the stopper (20), the opening (6) defining a peripheral edge (7) extending around the opening (6) and includes a distal axial end and a proximal axial end, the distal axial end forming the distal axial end (59) of the perforating tip (5) arranged on the longitudinal central axis (A) of the cannula (4).