Carter was injured in the last minute of the first period on a hit from Montreal Canadiens defenseman Jeff Petry during the Kings' 5-1 win. Carter has three assists in six games this season.
Los Angeles, which has won three straight, is the only NHL team without a regulation loss and has its best start in history.
With a win or overtime loss, the Kings would have points in seven consecutive games to open the season, which would tie their record set in 1995-96, when they started 4-0-3.
The Blue Jackets can establish their best start, bettering the 5-3-0 records in 2009-10 and 2010-11.