Brady was in uniform when he cut his thumb on his throwing hand before the game, Rapoport added.
"An accident occurred and Tom will be OK in time," Brady's agent, Don Yee, told Rapoport.
The Patriots quarterback did not join the team on the field. He was expected to see his first playing time of the preseason before suffering the minor injury.
After the game, coach Bill Belichick wouldn't go into specifics regarding why Brady sat out.
"I made the decision for him not to play," Belichick told reporters. "That's part of football. Things happen that are unexpected, and (Garoppolo) has been prepared for that since the day he got here.
"Sometimes things happen, things change, and you have to adjust to them. On offense, the quarterbacks refer to that as an audible."
Garoppolo played adequately in the preseason opener, completing 11 of 18 passes for 168 yards with no touchdowns or picks in the team's 34-22 win over the Saints.
Garoppolo put up those numbers without Julian Edelman in the lineup. The wideout isn't expected to play against Chicago, either, with NFL Media's Courtney Fallon reporting that the team is taking a cautionary approach with the left foot Edelman injured last week.
Brady, of course, is set to serve his four-game, Deflategate-related suspension to open the season. Until the Super Bowl-winning passer returns in Week 5 against the Cleveland Browns, this is Garoppolo's team.