Romo, who missed practice on Thursday and Friday, suffered the injury during last Sunday's 27-24 overtime win at San Francisco. He was also diagnosed with pneumothorax, otherwise termed a collapsed lung, but that has healed.
Romo will likely wear a protective vest if he plays Monday, as he did at halftime of the Cowboys' win over San Francisco.
The 31-year-old Romo, who missed more than half of the 2010 season due to a broken left clavicle, suffered his latest injury in the first quarter against the 49ers. He missed nearly the entire third quarter while getting treatment, but came back and rallied the team to overtime, connecting with Jesse Holley on a 77-yard pass play to set up Dan Bailey's game-winning field goal.
Romo went 20-of-33 for 345 yards and two touchdowns.