General manager Scott Howson announced the move on Wednesday prior to a home game against Los Angeles.
Moreau, 35, was injured at Phoenix on Jan. 4 in a 4-2 loss.
Formerly a captain at Edmonton, Moreau has one goal and four assists in 23 games with the Blue Jackets. The Huntsville, Ontario, native was claimed off waivers by Columbus from the Oilers last summer.
In 886 career NHL games, he has 146 goals, 136 assists and 1,082 penalty minutes with Chicago, Edmonton and Columbus.
The Blue Jackets have won five of six games, but still are five points behind a playoff spot in the Western Conference entering play on Wednesday.