Huget took to Twitter saying: "It's a real heart-breaker to pull out of France's summer tour to New Zealand, but I must have treatment on my Achilles tendon."
France coach Jacques Brunel is set to announce a 30-strong travelling party on Tuesday for a tour that will see Les Bleus play three matches against the all-conquering All Blacks.
France play New Zealand on June 9 in Auckland, a week later in Wellington and then on June 23 in Dunedin.
Huget, who has 51 caps for France, joins Brice Dulin, Maxime Machenaud and Francois Trinh-Duc on the injury list.
Others, including Louis Picamoles and Virimi Vakatawa, have scheduled operations and are also ruled out while Camille Lopez is still recovering from injury and Jefferson Poirot and Sebastien Vahaamahina are suspended.