Romo was forced out of action in the third quarter of the 20-17 loss to the Washington Redskins on Monday after taking a big hit to his back.
His injury was diagnosed as a contusion, and the team said that X-rays were negative.
Romo had surgery on his back twice in consecutive years earlier in his career, in 2013 to remove a cyst and last December to repair a disk injured in a game in Washington.
"We'll get the tests today, but we anticipate him being ready to go," Garrett told KRLD-FM in Dallas on Tuesday. "When we left the stadium last night, he seemed like he was okay, and we'll get the tests today to verify everything."
Garrett added that Romo eventually returning to Monday's clash after being sidelined for a period indicated that the injury was not serious.
"But they want to do some more extensive tests. We'll find out more as the day goes on," he added.
The Cowboys play at home against the Arizona Cardinals Sunday.