Carr's injury leaves a dark cloud over the best season for the Raiders (12-3) in 14 years.
Oakland clinched its first playoff berth since 2002 last week and can win the AFC West and earn a first-round bye by winning next week in Denver or if Kansas City loses one of its final two games.
But that is all secondary to Carr's health right now. The third-year quarterback has led a resurgence in Oakland with 28 TD passes and seven fourth-quarter comebacks this season.
Now the Raiders may have to prepare for life with Matt McGloin at quarterback.
Carr got hurt with Oakland leading 33-14 early in the fourth quarter when he was sacked by Trent Cole. Carr stayed on the ground for several minutes in pain as trainers came out to treat him.
With the crowd chanting "M-V-P! M-V-P!" Carr limped off the field without putting any pressure on his right leg. He was then taken away on a cart. There is no immediate word on the extent of the injury.
Carr's injury made it a down day all the way around. Andrew Luck threw two interceptions, Frank Gore lost a fumble and Indianapolis (7-8) allowed TDs on five straight drives to be eliminated from the playoffs for the second straight year.
Luck rallied the Colts from 26 points down to just eight with 2:33 left, but McGloin completed a 19-yard pass to Amari Cooper on third-and-8 on the next drive and the Raiders ran out the clock.
OUT OF NOWHERE: Rookie DeAndre Washington was a healthy inactive twice in the past four games as he fell behind fellow rookie Jalen Richard on the Raiders depth chart. With injuries at other spots, Washington has gotten the chance to play the past few weeks and is making the most of it. He ran for 99 yards on 12 carries and scored on a pair of 22-yard runs in the third quarter.
OPPORTUNISTIC PLAY: The Raiders turned two interceptions by Luck into two touchdowns in the first half.
Luck twice forced throws while under pressure and Nate Allen intercepted the first and Reggie Nelson got the second in the end zone. Carr made the Colts pay for those mistakes, connecting on TD throws to Andre Holmes and Jalen Richard on the ensuing drives.
MISSED KICKS: Sebastian Janikowski had made 266 of his previous 267 extra point attempts before missing twice in the second quarter. He was wide left after one touchdown and then had another attempt blocked in the final minute of the half for the Raiders. After making a PAT in the third quarter, Janikowski threw out his arms in celebration.
BOTCHED FAKE: The Colts bypassed a chance at early points when coach Chuck Pagano opted to call a fake rather than attempt a 48-yard field goal on the second drive. Holder Pat McAfee got stopped for no gain on the play.
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Raiders lose Carr for season in win over Colts
Derek Carr leaves the game in the fourth quarter with a broken fibula as the Raiders defeat the Colts 33-25.
Del Rio announces that Carr broke his fibula
Jack Del Rio discusses the Raiders' bittersweet victory after Derek Carr broke his fibula and is out indefinitely.