The injury leaves the Cowboys (4-2) with 40-year-old Brad Johnson as the starter. Johnson, who won a Super Bowl with Tampa Bay, hasn't started a game since 2006 in Minnesota.
Romo missed on three straight passes to start the overtime, but before then passed for 321 yards and three touchdowns despite heavy pressure. He was sacked three times and hit several other times. Through Sunday's games, Romo ranks second in NFC passing with a 103.5 rating. He has thrown for 14 touchdowns and been intercepted five times.
In 2007, his first full season as a starter, Romo led the Cowboys to a 13-3 record, best in the NFC. They lost to the Giants in the playoffs.
Johnson quarterbacked the Tampa Bay Buccaneers to the NFL championship in 2002. He has been Romo's backup since last season and threw only 11 passes in 2007.