Bowers will be eligible to return to the active roster on Monday, Nov. 3.
In his fourth year out of Clemson, Bowers has six tackles, one sack and one fumble recovery in five games this season.
He will join suspended Buccaneers fullback Jorvorskie Lane in sitting out Sunday's home game against Minnesota, as well as the game at Cleveland. Lane's two-game ban for violating the same policy was announced last week, when Tampa Bay had a bye.
Lane will be eligible to return to the active roster on Nov. 3 as well.
The Associated Press contributed to this report.