In the team's statement, the Clippers said there is no timetable for his return.
Leonard suffered the injury during Game 4 of the NBA Western Conference Semifinals against the Utah Jazz. He missed the Clippers' final eight playoff games with what the team called a sprained right knee.
Despite the absence of Leonard, the Clippers rallied from a 2-0 series deficit to beat the Jazz in six games. Los Angeles then lost in six games to the Phoenix Suns in the Western Conference Finals.
Leonard, who averaged 30.4 points, 7.7 rebounds and 4.4 assists over 11 postseason games this year, has a player option for the 2021-22 season.
The 30-year-old Leonard, a two-time NBA champion who was named NBA Finals MVP in those title runs, had averages of 24.8 points, 6.5 rebounds and 5.2 assists in 52 regular-season games this year.