He is the third Panthers player to be suspended this week. On Monday, Panthers defensive end Wes Horton was suspended four games for violating the NFL policy on performance-enhancing substances.
Injured wide receiver Stephen Hill was suspended one game for violating the NFL's policy and program for substances of abuse.
Alexander, who is on injured reserve, was suspended twice last season for substance abuse violations.
Alexander was drafted out of Oklahoma in the fourth round in 2012.