A timeline for surgery hasn't been established, but Cousins' 2019-20 season is in jeopardy, Wojnarowski notes.
Cousins was bumping knees with another player while working out in Las Vegas on Monday and had to leave the court, a source told Wojnarowski.
TMZ Sports later obtained footage of the moment Cousins' suffered the injury.
The four-time All-Star was limited to 30 regular-season games with the Golden State Warriors last season following a one-year layoff due to a ruptured left Achilles tendon he suffered in January 2018 while playing for the New Orleans Pelicans. Cousins then tore his left quad muscle during the Warriors' first-round playoff series against the Los Angeles Clippers in April.
Cousins, who turned 29 on Tuesday, signed a one-year contract with the Lakers in July for just above the veteran's minimum.