Odom was diagnosed Wednesday by team orthopedist Dr. Steve Lombardo, a day after the 6-foot-10 star was hurt in a 102-94 victory at Houston.
Odom is averaging a career-high 17.5 points and 8.7 rebounds this season.
He was injured in the first quarter when he landed awkwardly after Shane Battier blocked his shot on a drive. Odom stayed in the game for another 90 seconds, but the Lakers called a timeout to pull him.
"I felt like something was really wrong," Odom said after the game. "I've never had anything like this."
Odom had started all 20 games for the Lakers and is averaging 18 points and nine rebounds per game.
Lakers coach Phil Jackson felt the injury was serious after the game.
"He's going to miss some time," he said. "I'll be really happy if he plays again in January."