The third-year player will be able to return to the active roster on Monday, Sept. 29 -- following the team's Week 4 game at Baltimore.
He remains eligible to participate in the team's offseason and preseason practices and games.
"I recently learned that I tested positive for a substance that is banned by the NFL. The NFL policy is strict, and I have chosen to take responsibility," Alexander said Monday in a statement. "I sincerely apologize to my teammates, coaches, and Panthers fans for the effect of my mistake on the team. I will continue to work extremely hard in all team workouts, training camp, and the pre-season with my team. During the suspension, I will stay in top football shape and be ready to contribute immediately upon my return."
Alexander has six starts and 3.5 sacks in two seasons. He is the first Carolina player suspended for violating the substance abuse policy since defensive tackle Andre Neblett in July 2012.
Alexander was slated to be a backup to ends Greg Hardy and Charles Johnson. While his suspension may not be a factor in Carolina's draft plans, general manager Dave Gettleman said earlier in the week that if a "blue goose'' defensive end or pass-rusher was the best player available with the 28th pick of next week's draft, he wouldn't hesitate to pick him.
Team officials and Alexander's representatives were unavailable for comment on the suspension.