Avery, known for his aggressive play and off-ice comments, was sent to New York's American Hockey League affiliate in Connecticut.
The Rangers made the announcement while the team was in Sweden preparing for Friday's season opener in Stockholm.
The nine-year NHL veteran is in the final year of a four-year, $15.5 million contract he signed with the Dallas Stars in 2008.
Avery, 31, has racked up 87 goals, 157 assists and 1,512 penalty minutes in 565 career games for Detroit, Los Angeles, Dallas and the Rangers.
Last season he notched three goals and 21 assists while piling up 174 penalty minutes in 76 games.
The Rangers also revealed that star defenseman Marc Staal had been placed on injured reserve due to recurring headaches related to a concussion he suffered last season.