The assembly comprises a body forming a reservoir for the liquid, the body being provided with a liquid-injection needle, a plunger mounted to be axially movable in the body between a ready position and an end-of-injection position, and a sheath in which the body is mounted to be axially movable between an active position in which the needle projects from a distal end of the sheath, and a protecting position in which the needle is retracted inside the sheath. The assembly also comprises means for axially securing the plunger and the sheath in a relative position of said plunger and said sheath serving firstly to position the body in its protecting position relative to the sheath and secondly to position the plunger in its end-of-injection position relative to the body.