X-rays showed Romo did not suffer any breaks resulting from hits by Giants defensive linemen Justin Trattou and Mathias Kiwanuka late in the second quarter. After the game, Romo said he would be fine and ready to play at Kansas City in Week 2.
"I've been told that they're negative, which is a positive, meaning not broken, so that's a good thing," coach Jason Garrett said of Romo's X-rays.
Garrett said he did not anticipate Romo wearing any additional padding this week. Romo already wears a rib protector. In 2011 he wore an extra protective vest after suffering a fractured rib and punctured lung against San Francisco in Week 2.
"There really was no doubt in my mind that he was going to go back in the game and play," Garrett said. "When I heard it was a rib, I said, 'You know, he'll be OK.' Kyle Orton got one snap right before halftime but Tony just shook it off and came back and played the second half ... Tony has a track record for us not only fighting through it but playing well with the injury."
Also, Cowboys wide receiver Dez Bryant suffered a sprained foot late in the fourth quarter.
Bryant, who finished with four catches for 22 yards, had X-rays at AT&T Stadium on Sunday night that were negative. Bryant said he wasn't sure if he would practice Wednesday but expects to play against the Chiefs.
Garrett was not sure of the extent of Bryant's sprained foot. On Monday afternoon, Bryant had an MRI, which confirmed he suffered a slight foot sprain, a league source told ESPN.
The recovery time for a sprained foot varies. In 2012, running back DeMarco Murray missed six games with a sprained foot. Lance Dunbar suffered a sprained foot on Aug. 17 in a preseason game against Arizona and is hoping to practice for the first time since Wednesday. Dunbar said he expects to return for the Chiefs.
Garrett said he did not believe Bryant's injury was "too serious."
"He seems to be walking around OK today," Garrett said, "and we'll see how he is over the next couple of days."
In a Week 2 win at San Francisco in 2011, Romo suffered a cracked rib and punctured lung that required him to wear a protective vest for weeks. He also took pain-killing injections before games. In last year's season finale at Washington, Romo suspected he suffered a broken rib but did not come out of the game.
"That was one that I felt all over," Romo said Sunday night of his 2011 rib injury. "I wouldn't put this one in that class."
Meanwhile, cornerback Morris Claiborne will not require surgery on his left shoulder, according to a source, but he will likely wear a harness of sorts for added protection. Claiborne missed a few snaps after getting hurt in the third quarter but was able to return.
ESPNDallas.com's Calvin Watkins and ESPN NFL Insider Ed Werder contributed to this report.