Campbell landed hard on his shoulder after being hit at the end of a scramble by Cleveland linebackers Chris Gocong and Scott Fujita with about 4 minutes remaining in the half. Campbell stayed down on the turf after the hit and was then helped to the locker room.
Tests determined that he broke his collarbone.
"I'm not going to let this football team blink," coach Hue Jackson said after a 24-17 victory.
"We'll miss Jason for a little while. I have no idea how long it will take. I don't know. We'll see as we go. I know, obviously, he won't be here next week or anything like that. We'll continue to press forward and get better."
Campbell was replaced by Kyle Boller, who went 8-for-14 for 100 yards in his first action of the season.
"I felt very comfortable," Boller said. "I probably was a little bit quick in the beginning. Wish I could slow my feet down a little bit, but that's part of it. I felt like in the second half I got more comfortable each play, and even in the last couple drives it felt good."
The only other quarterback on Oakland's roster is rookie Terrelle Pryor, who will be activated Monday. Pryor got a one-week roster exemption after serving a five-game suspension to start his career.
Campbell has completed 60.6 percent of his passes for 1,170 yards with six touchdowns and four interceptions this season. Campbell is in the final year of his contract.