The Bears fear Smith suffered a torn pec and he is scheduled to undergo an MRI, NFL Network's Ian Rapoport reports.
Smith, the eighth overall pick in the 2018 draft, left the prime-time matchup in the first quarter and didn't return.
He entered the game with 98 tackles, two sacks, and an interception.
If Smith misses significant time, it would be a major blow to the Bears who still have a slim chance of making the playoffs.
Chicago's defense is already dealing with several injuries on defense.
Linebacker Danny Trevathan (elbow) and cornerback Prince Amukamara (hamstring) missed Thursday's game. Meanwhile, Pro Bowl defensive lineman Akiem Hicks (elbow) has been sidelined since Week 5, though he's nearing his return.