Romo suffered a fractured rib in last Sunday's 27-24 overtime win at San Francisco. He was also diagnosed with pneumothorax, otherwise termed a collapsed lung.
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.
Wide receivers Miles Austin (hamstring) and Dez Bryant (thigh), center Phil Costa (knee), guard Derrick Dockery (knee), running back Felix Jones (shoulder) and cornerback Orlando Scandrick (ankle) also missed practice Thursday.
Dallas plays Washington on Monday night.
Dockery suffered a fractured tibia and sprained MCL in the third quarter of last Sunday's victory.
Dockery made his first start of the season at guard in place of Bill Nagy (neck), who was back at practice Thursday.
The starter entering the regular season, Nagy should be ready to play Monday night against the Redskins.
Without Dockery, rookie David Arkin will backup Nagy at guard.