The Clippers and Leonard will decide on the course of treatment for the injury within the next two weeks, sources told ESPN's Adrian Wojnarowski.
Leonard did not play in the final three games of the Clippers' first-round series against the Phoenix Suns because of the injury suffered in Game 1. The Clippers, who lost four straight after opening the series with a win, had said Leonard had a right knee sprain.
Leonard played through the injury in Game 2 before being ruled out for Games 3-5. The Clippers were eliminated with a 136-130 loss Tuesday.
The injury was compounded by the loss of Paul George, who has not played since March 21 because of a right knee sprain.
"It's always in the back of your mind, 'What if.' It's easy to say, 'What if,' because a lot of guys get hurt," Clippers coach Ty Lue said Tuesday night. "It's just been our luck the last three years."
The Clippers had Leonard and George together on the floor only 38 times this season, going 24-14 in those games.
This is the second time in three seasons that Leonard has suffered a right knee injury during the playoffs. He suffered a partial tear in his right ACL during the 2021 Western Conference semifinals before undergoing surgery in July 2021 and missing the 2021-22 season.
Leonard, 31, averaged 23.8 points, 6.5 rebounds and 3.9 assists in 52 games (50 starts) in 2022-23. He has not played more than 60 games in any season since 2016-17.
The Athletic first reported on Leonard's latest injury.
Information from ESPN's Ohm Youngmisuk and Reuters was used in this report.