The four-time All-Star's entire 2019-20 season is in jeopardy considering his recent injury history and the typical nine-month recovery window.
Cousins, 29, signed a one-year deal with the Lakers in free agency after a season with the Golden State Warriors. He missed the first half of the 2018-19 season with a torn Achilles.
Cousins was injured when he bumped knees with another player while working out on Monday, ESPN reported.
In nine NBA seasons, Cousins has averaged 21.2 points and 10.9 rebounds per game. Joining the Lakers on a $3.5 million pact reunited Cousins with former New Orleans Pelicans teammate Anthony Davis.
Cousins also missed several weeks during the 2019 NBA playoffs with a quadriceps injury.
--Field Level Media