Brady sliced the thumb on his right throwing hand 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 CSN New England.
A source confirmed the report and said that Brady "will be OK 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.
"I made the decision before the game to just play Jimmy and Jacoby," Patriots coach Bill Belichick said.
When asked about the report of Brady slicing his thumb, Belichick said: "I made the decision for him not to play tonight."
Brady did not play in the team's preseason opener against the New Orleans 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 turns 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.