Bush, who passed the 1,000-yard rushing mark for the first time in his career this season, missed practice all week and was ruled out of the game on Friday.
He was acquired in a trade from New Orleans in July and helped lead a late- season surge that pulled Miami out of an 0-7 hole, averaging nearly 94 yards over the last eight games as the Dolphins went 5-3 during the stretch.
Bush, 26, averaged almost 130 yards in his last four games of the season, which included a 203-yard effort in a Week 15 win over Buffalo.
He finished with 1,086 yards and six touchdowns on 216 carries with 43 catches for 296 yards and a score. His previous career-best was 581 yards rushing for the Saints in 2007.
The Dolphins (5-10) have a chance to knock the Jets (8-7) out of playoff contention in Sunday's home game. New York needs a win and some help to qualify for the postseason.