Brady sliced his thumb with a pair of scissors trying to pry something from his cleats before taking the field. It is not known if he required stitches, according to CNS New England.
A source confirmed the report and said that Brady "will be okay in time."
Coach Bill Belichick had said in his pregame interview on 98.5 The Sports Hub that the team would play all three quarterbacks, and earlier in the day, ESPN.com reported that Brady was expected to start.
Brady did not play in the team's preseason opener against the Saints after being excused to attend the memorial service of a family member.
The veteran quarterback will serve a four-game suspension to begin the regular season, as the team will turn to Garoppolo as its starter. This will mark the first season since 2001 that a quarterback other than Brady starts the regular-season opener for the Patriots.
Thursday night's game also will conclude a week of activity between the Bears and Patriots, as they conducted joint practices on Monday and Tuesday, while Wednesday they held a joint walk-through-style practice.
The Patriots have divvied up reps between both Garoppolo and Brady with the first-team offense throughout training camp and preseason. Brady will not be allowed to practice or be at the facility during his suspension, with the preseason marking his last extended action with his teammates until reinstatement in Week 5.