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 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.
The Associated Press contributed to this report