Romo has a herniated disk in the lumbar region and needs to have surgery, a source told ESPN Senior NFL Insider Chris Mortensen.
Dr. Michael Kaplan, who has not evaluated Romo, said an operation for an injury of this nature is 95 percent predictable with a three to four month recovery.
At his weekly news conference, coach Jason Garrett wouldn't rule Romo out, instead saying he would receive treatment each day this week and the team would evaluate the quarterback's injury each day.
"We have not made that determination at all at this point," Garrett said when asked about ESPN's report. "Like with any player, the day after a game you just want to see what the injury is and we've done that with Tony and we want to get him involved in treatment as quickly as we can and we started that process."
Orton has 69 career starts and is 35-34. He hasn't started since the 2011 regular-season finale with Kansas City.
"Feel great about Kyle Orton," Garrett said. "We'll evaluate Tony on a day by day this week. In the meantime Kyle will be the guy that's taking the snaps until Tony is ready to go. Again that's what we do at every position is get ready to go and get ready for the next opportunity that we have and obviously it's Philadelphia Sunday night."
Garrett said the Cowboys likely will sign another quarterback this week, as Orton is the only backup on the roster.
The Cowboys are scheduled to work out free-agent quarterbacks John Skelton and David Carr on Tuesday, a source told Schefter. They have also invited Tyler Thigpen to workout this week, according to multiple reports.
Romo said Sunday he would undergo an MRI on his back Monday but didn't believe the injury would jeopardize his availability for the Philadelphia game.
Romo said his back, which was sore going into Sunday's comeback victory over the Washington Redskins, began to bother him after a hit in the first half.
"That triggered it a little bit," Romo said Sunday. "Whatever the kid did on that one play, it really sent something that didn't feel comfortable. But it's in a completely different spot than the back stuff I had last year, so that's a good sign."
Romo had surgery in April to remove a cyst from his back and did not take a snap until the team reached training camp in July.
Garrett said the team does not believe there is any connection from the back surgery Romo had last spring to this injury. Romo had a sore back in practice last week, but Garrett said it "never got to the point where it took him out of anything." Romo was not on the injury report.
Romo was limping as he carried out fakes on running plays against Washington. He also appeared to kick the back of his leg after spinning free from the pocket on a third-down pass to Miles Austin.
Romo completed 17 of 27 passes for 226 yards, including the winning touchdown to DeMarco Murray on fourth-and-goal from the Washington 10 with 1:08 to play.
Longtime teammate Jason Witten admired Romo's toughness after news of the extent of the quarterback's injury had been learned.
"A lot of times you lose sight of [Romo's toughness], what Tony is all about, the kind of toughness that he shows day in and day out, not only mentally but physically, you just commend him how he approaches it, just resilient to find a way and he's so good in those situations and kind of put the team on his back."
Romo has dealt with numerous injuries over the years, including a broken rib in 2011. He hurt his ribs again in last season's season-ending loss to the Redskins, a result that kept the Cowboys from making the playoffs.
ESPN.com Cowboys reporter Todd Archer and ESPNDallas.com's Calvin Watkins contributed to this report.