IRVING, Texas -- Dallas Cowboys quarterback Tony Romo has a broken finger on his throwing hand and could be out as long as four weeks.

Romo, who had started 30 straight regular-season games since replacing Drew Bledsoe in 2006, broke his right pinkie on the first play of overtime in a 30-24 loss at Arizona on Sunday.

"We don't know how long he'll be out. It depends on how fast that heals," coach Wade Phillips said Monday.

"I'd say week to week, depending on quickly he heals. Different people heal differently."

The injury, which Phillips said won't require surgery, 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.

"It's unfortunate for Tony to have to go through something like this," Johnson said. "He'll recover quick, he has a great attitude about it.

"At this time, it's really just important for the offense especially to just kind of catch on to my snap count, and the way we manage the huddle."

The Cowboys had no plans Monday to sign a veteran quarterback or trade for one before Tuesday's trade deadline, a team source told ESPN's Michael Smith.

Romo missed on three straight passes to start the overtime, having passed for 321 yards and three touchdowns in regulation despite heavy pressure. He was sacked three times and knocked down 19 times.

"Obviously, he had trouble throwing the ball that last series in overtime," Phillips said.

Romo, whose hand was heavily wrapped after the game, fumbled three times Sunday, losing one, but -- for the first time in nine games -- didn't throw an interception.