Carter, who is expected to be out at least one week, is tied for the team lead with five goals and is fourth with nine points in 14 games.
"I didn't know [about the injury] until this morning, actually," Kings center Anze Kopitar told Rosen. "I saw him walking in with a boot, and that was it."
If Carter goes on IR, it would be the first time since he separated his shoulder as a member of the Columbus Blue Jackets in January 2012.
"With Jeff, the guy going down, it's definitely a loss for us. But that’s the way it is, and we're going to have to find a way to score goals and put up points and win hockey games at the end of the day," Kopitar said. "With him or without him we're going to have that, but it's certainly a loss."