In a statement, Wright said he used the drug Adderall in July for "health issues I was experiencing." Adderall is on the NFL's list of banned drugs.
Wright is the second Tampa Bay starter disciplined for using Adderall. Cornerback Aqib Talib was suspended Oct. 13 for four games and subsequently traded to the New England Patriots while serving the ban.
Wright signed a five-year, $37.5 million contract with the Bucs as a free agent in March. He started the first 10 games of the season before sitting out Sunday's 24-23 loss to Atlanta because of an Achilles tendon injury.
Losing the six-year veteran will be a blow to a Buccaneers defense that has struggled against the pass this season. The Bucs will have to lean on cornerbacks Brandon McDonald and Myron Lewis with Wright gone.
The Associated Press contributed to this report