Romo, 33, aggravated a back problem during Sunday's 24-23 win over Washington that kept their playoff hopes alive. However, they must defeat the Philadelphia Eagles in their final regular-season game Sunday in Arlington, Texas, to make the playoffs.
ESPN cited an unnamed league source Monday as saying Romo's injury was a herniated disk that required surgery and would sideline him for the rest of the year. Garrett said Romo had an MRI Monday and was receiving treatment for "a hip or back-type injury."
Garrett, at a news conference, said, "Like with any player a day after the game, we want to see what the injury is and we've done that with Tony."
He also said, "We'll evaluate him on a day-by-day basis and make the best decision for our team."
Romo had a sore back prior to Sunday's game against Washington but said after the game it was worse after a first-half hit. He finished the game, completing 17-of-27 passes for 226 yards and two touchdowns on the day.
His touchdown pass to DeMarco Murray with 1:08 to play provided the winning points against Washington.
Kyle Orton is the only other quarterback on the Dallas roster. He's just 3-of-5 passing this season with 40 yards. Orton, who has appeared in just three games in the last two years, was a starter for Chicago and Denver earlier in his career.
Romo has played his entire 10-year career with the Cowboys. He has completed 342-of-535 passes for 3,828 yards and 31 touchdowns while being intercepted 10 times. For his career, Romo is 2,439-of-3,775 for 29,565 yards and 208 touchdowns.
Swim Week Miami Beach 2014 [PHOTOS]