The outside linebacker suffered the injury making a tackle on a kickoff return in the final minute of Sunday's 27-23 victory at Seattle.
"It'll probably be at least a week, and then we'll see how he reacts to all the treatment," coach Ron Rivera said on Wednesday. "We were very fortunate. He is very fortunate that it wasn't as bad as it looked, thank goodness."
Rivera didn't want to give a timetable on Thompson's return for the 5-0 Panthers.
"If he can get the swelling down, the movement back, it would be a week, two weeks, three ... who knows," Rivera said. "I really couldn't give you a timetable. And it would be unfair to the kid to give him a timetable and create expectations."
Klein missed the Seattle game with a concussion, but he was cleared to practice in all non-contact drills on Wednesday and appears on track to be cleared for Sunday.
Klein suffered the concussion three weeks ago against Tampa bay.
The status of defensive tackle Dwan Edwards is in doubt after he suffered an ankle injury against Seattle. The injury occurred on a play that Rivera would like to see the league changed to prevent injuries.
He said it is not necessarily a chop block, as Edwards described it.
"What it is, it's a block where one guy's engaged and the next adjacent blocker by the rules right now is allowed to come down low and cut block," Rivera said. "There's some controversy as to whether that should continue to be allowed or not.
"There's a lot of us that don't think it should be just because of that."