Carter, who is listed as week-to-week, has posted just three assists in his first five games with Columbus, which gave up Jakub Voracek and two draft picks to acquire him from Philadelphia in June.
The seventh-year veteran aggravated an old injury during this past Saturday's game against Dallas after blocking a shot.
Columbus also added goaltender Mathieu Corbeil to the roster on emergency recall from the Saint John Sea Dogs of the Quebec Major Junior Hockey League (QMJHL).
Corbeil was recalled because of goaltender injuries throughout Columbus' organization. According to the Columbus Dispatch, Curtis Sanford -- who has been serving as Steve Mason's backup while Mark Dekanich is on IR with an ankle injury -- sustained a groin strain in Monday's practice.
Additionally, the Dispatch reported that Allen York cannot be recalled from Columbus' AHL affiliate in Springfield because of a shoulder injury he suffered this past weekend.
Corbeil was the Blue Jackets' fifth pick in the 2010 draft. According to the Dispatch's report, he can be with Columbus for only 24 hours before being returned to his junior league team.
The 20-year-old Corbeil has gone 7-2-0 with a 2.61 goals-against average with the Sea Dogs this season.