A fluid dispenser comprising: a fluid reservoir (1); and a pump (3) comprising a pump body (30) and an actuator rod (34), defining between them a pump chamber (33) having a predetermined maximum volume, the rod (34) being axially movable in the body (30) so as to vary the volume of the pump chamber (33); the dispenser being characterized in that it further comprises a dispenser cannula (5) that is mounted on the actuator rod (34) and that includes a dispenser outlet (52) that is suitable for forming a drop of fluid that separates from the cannula (5) by gravity, the determined maximum volume of the pump chamber (33) being substantially equal to the volume of the drop of fluid that is dispensed at the dispenser outlet (52).