The Buccaneers placed the seventh-year pro on the non-football injury list Tuesday. The team also signed cornerback Marcus McCauley and released cornerback Derrick Roberson before re-signing him to the practice squad.
Askew started two of five games he played in this season, carrying the ball once for no gain. He sat out Sunday's loss to the Carolina Panthers with neck and back pain.
Last week, coach Raheem Morris said the player had been injured in a "fender bender" accident.