The New York Rangers assigned Avery to the Connecticut Whale after the veteran winger cleared waivers on Saturday.
Avery started the season in the AHL before getting recalled by the Rangers on Nov. 1.
The 31-year-old had three goals and 21 penalty minutes in 15 games.
He was a healthy scratch for nine straight games before being placed on waivers.
Avery is in the final year of a US$15.5-million, four-year contract.