An automatic fluid injection device having a body fastened to a support. The body containing one or more fluid reservoirs, each containing an injection piston; a needle assembly including an injection needle; and an injection mechanism. The needle assembly including an injection needle and an insertion actuator made of a shape memory alloy. The injection mechanism having a retraction ring; a needle support; an insertion ring; a retraction spring; an actuator ring; and an insertion spring. The insertion spring and the retraction spring retained, at rest, in their compressed state, activation of the actuator by heating to about 50% of the available contraction causing the needle support to be released, and activation of the actuator by heating to reach 100% of the available contraction causing the insertion ring and the assembly formed of the needle support and of the injection needle to be released.