In his place, Kareem Hunt will get the start.
"You never want to see a guy like Nick go down," Hunt said. "Definitely, what he means to this team is crazy. We've got a lot of good backs. We should be able to hold it down until he gets back."
After Friday's practice, coach Kevin Stefanski was not ready to say whether Chubb would have to go on injured reserve, which would force him to miss at least three games.
Browns wide receiver Jarvis Landry took a step in his recovery from a knee injury, as he was designated to return from injured reserve Friday, clearing the way for him to rejoin practice. Stefanski said he wouldn't rule out the possibility of Landry being activated to play against the Cardinals.
Chubb ranks second in the NFL with 523 rushing yards this season. He is averaging 5.8 yards per carry with four touchdowns.
Hunt has 295 rushing yards, averaging 5.4 yards per carry. He was the 2017 NFL rushing champ while with the Kansas City Chiefs.
Landry suffered a medial collateral ligament sprain in his left knee on the opening drive against the Houston Texans on Sept. 19. He has missed the past three games and has six catches for 80 yards this season.