A fluid dispenser head for mounting on an axial actuator rod (31) of a dispenser member (3), the head comprising an inner core (1) and an outer casing (2), the core (1) forming a connection sleeve (11) of axis (X) for mounting on the axial actuator rod (31), the casing (2) forming a dispenser endpiece (23) that is elongate and that is offset relative to the axis (X), the dispenser head being characterized in that the core (1) forms a deformable cannula (14) that is connected to the connection sleeve (11) and that extends in the endpiece (23) of the casing (2), said cannula forming a first section (14a) that is substantially rectilinear and that extends transversely relative to the axis X, a second section (14b) that is bent, and a third section that is inserted into the dispenser endpiece (23), the cannula (14) initially being rectilinear over its entire length and then being deformed while it is being inserted into the endpiece (23).
