It is the third suspension for Alexander, who suffered a season-ending Achilles injury during a preseason game against the Miami Dolphins.
Alexander was suspended the first four games of last season and then 10 more for a second offense. Carolina's 2012 fourth-round pick admitted earlier this year that marijuana use was the reason for last season's suspensions.
Alexander was set to become a restricted free agent in March.
Alexander is the third Carolina player to be suspended by the league in two days.
Wide receiver Stephen Hill, who suffered a season-ending knee injury in training camp, was suspended for one game after he was cited for possession of drug paraphernalia during a traffic stop in July.