Rondo, who suffered the injury during practice Sunday evening, will undergo surgery this week. The recovery timeline could keep him on the sidelines until the second round of the playoffs.
The Lakers won't be permitted to replace Rondo with a substitute player, ESPN's Bobby Marks notes.
The 34-year-old is averaging 7.1 points, five assists, and three boards during his second campaign with the Lakers. The Lakers' backcourt is already missing Avery Bradley, who opted out of the NBA restart citing concerns over the health of his family.
Rondo agreed to a two-year, $5.1-million deal this past offseason, which includes $2.6-million player option for 2020-21.