The injury occurred in the first quarter of Tuesday night's 102-94 win over the Houston Rockets.
He landed awkwardly while following his own missed shot and was taken to a hospital where an MRI revealed the extent of the injury. He is using crutches to walk.
"I don't know exactly when it happened, on my way up or on my way down, but I guess I just twisted it up, sprained my MCL pretty good," Odom told the Los Angeles Times after his return from the hospital to see the end of the contest.
In 21 games this season, Odom, a first round draft pick out by the Los Angeles Clippers in 1999 out of Rhode Island, averaged 17.5 points, 8.7 rebounds, and 4.9 assists.
He has been called the league's most improved player to date.