Colts spokesman Avis Roper said the team had no comment after the league's announcement.
Brazill was suspended for the first four games last season for violating the substance abuse policy. He said at the time it was for marijuana use.
Brazill played in 10 games last season, finishing with 12 catches for 161 yards and two touchdowns. In two seasons, he has 23 catches for 347 yards and three touchdowns. He was drafted in the sixth round out of Ohio University in 2012.