Per Grace Raynor of the Post and Courier, Bryant missed practice on Monday and Tuesday after head coach Dabo Swinney made the change.
Raynor noted Swinney gave Bryant the day off Monday "to process the news and have an afternoon to himself."
Per NBC Sports' Kevin McGuire, Swinney noted after making the change he intends to keep Bryant in the Tigers' game plan moving forward.
Bryant, who is now in his senior year, has started each of Clemson's first four games in 2018. He's thrown for 461 yards, rushed for 130 yards and accounted for four touchdowns.
Per ESPN's David Hale, the NCAA's four-game redshirt rule means Bryant can't appear in another game for Clemson if he wants to transfer to a program that will give him an opportunity to start.
"If he walked in here today and said, 'Hey coach, I don't want to play the rest of the year unless you've got to have me,' OK. If that's what you want to do, I'm all for it because I love Kelly," Swinney said, via Raynor. "I would be disappointed in that because we need him, but I wouldn't judge him for that."
Lawrence, who was the top-ranked player in the 2018 class by 247Sports, has thrown for 600 yards and nine touchdowns on just 60 attempts.
The Tigers are currently ranked No. 3 in the Associated Press Top 25 poll with a 4-0 record. They finished last season 12-2 with Bryant as their starting quarterback but lost to Alabama in the College Football Playoff semifinal.