McClain was found in violation of the league's policy against substances of abuse.
"I apologize to my family, the Cowboys organization, my teammates and Cowboys fans for my mistake," McClain said in a statement via the NFL Players Association. "I will not break the rules of my profession in the future, and I regret my error. I look forward to returning to the field on week 5, when I hope to help my team beat the Patriots."
McClain had a renaissance of sorts last year in Dallas after two separate retirements. His 81 tackles over 13 games helped negate the loss of linebacker Sean Lee and propel the Cowboys into the playoffs. He signed a one-year deal to remain in Dallas but was already facing a four-game fine for his third failed drug test.
Now, his troubles in Dallas have gotten worse. Another failed test activated Thursday's suspension.