The device has a protection sleeve (34) and a support (36) that are displaceable axially with respect to each other between a needle releasing position and a needle retracted position. The support has a rotative integrating unit with a pawl (66) elastically returned to a position in which the pawl is cooperated with a complementary axial groove (64). The protection sleeve and the support have complementary rotative integrating units (70) that are activated when the protection sleeve and the support are in the needle releasing position.