ESPN reported Monday that the passer was expected to miss about four weeks of action because of a broken finger on his throwing hand. The team's backup quarterback is Brad Johnson.
Romo was battered by Arizona's defense throughout the Cardinals' 30-24 overtime win Sunday, getting sacked three times and hit eight times.
According to multiple media outlets, Romo was seen with his right hand heavily wrapped with ice in the locker room following the game.
The team's official Web site said Romo sprained his right pinky finger during the first play of overtime, when he was sacked by Chike Okeafor. Romo fumbled the ball after the sack but was able to recover it.
He stayed in the game and then threw two incompletions to Terrell Owens before the Cowboys were forced to attempt a punt.
Cowboys head coach Wade Phillips was expected to give his weekly news conference at 1 p.m. CDT.
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The Dallas Cowboys are neither confirming or denying the reports, refresh this story for updates from nbcdfw.com.