The Browns host the Cincinnati Bengals with snowy weather forecast in Ohio.
Griffin started and finished the Week 1 loss to the Philadelphia Eagles but on one of his five rushing attempts, suffered a broken bone in his left shoulder. He was placed on injured reserve with a return designation and was cleared for contact on Nov. 29. He practiced that day and again Monday and Wednesday this week.
"It's been awhile since I've been back out but the guys around me are going to make this a smooth transition," Griffin said Thursday after coach Hue Jackson confirmed the move. "We're all out there fighting for each other. They know not one guy can do this by himself and make a world of difference."
Griffin was 12-of-26 for 190 yards in the Browns' Week 1 loss to the Eagles.
"I've had a couple slides here and there, but no 350-pounders have landed on me yet," Griffin said. "It's just something you've got to be ready for."
The Browns, who are coming off a bye week, are 0-12 and desperately want to avoid being the first team since the 2008 Lions to go 0-16.
This is Griffin's first season in Cleveland after spending his first four NFL campaigns with the Washington Redskins.
The Browns would like to get a look at how Griffin fares in the final four games before deciding on how to address its quarterback situation in the offseason.
Jackson acknowledged protection problems might make him hesitant to activate RGIII, who had been on the injured reserve/designated to return list.