Bennett said he made the decision for personal reasons. He met twice with new Sun Devils coach Herm Edwards, who said in a prepared statement that he hoped Bennett would remain on staff.
"Family always comes first, and right now he needs to turn his attention to that," Edwards said in the statement.
Bennett, 62, is completing his first season as Sun Devils defensive coordinator after coming over from Baylor, where he held the same post for the previous six seasons. He was hired by Todd Graham, who will remain Arizona State's head coach for the bowl game before departing.
Bennett, who has a home in College Station, Texas, informed Edwards of his decision Tuesday morning.
"I will always be a Sun Devil fan," Bennett told reporters Tuesday. "I will pull for these kids and this program. I think it's in good hands. Just very appreciative to all of them."