The league did not specify which comments violated the anti-tampering rule.
Rivers compared Leonard to Michael Jordan while breaking down the Raptors' matchup with the Golden State Warriors on ESPN's NBA Finals preview show.
"He is the most like Jordan that we've seen," Rivers said after Magic Johnson, the Lakers' former president of basketball operations, talked about Leonard on Tuesday's preview show. "Like, there's a lot of great players. LeBron [James] is phenomenal. KD [Kevin Durant] is phenomenal. But he is the most like him.
"Big hands. Post game. Can finish. Great leaper. Great defender. In-between game. If you beat him to the spot, bumps you off. Then you add his 3-point shooting. I never get into who's the best player. Magic is the best player, Michael Jordan is the best player, LeBron. But it's that same group."
Leonard will be a free agent this summer.
NBA commissioner Adam Silver said Rivers "crossed a bright line" when asked what the Clippers coach should do when he appears on a show that would require his analysis of other teams' players.
"I would just say Doc has been at this for a long time," Silver said in a video posted by the Boston Globe on Friday. "It's not a fun part of my job ever fining anyone. And I understand the interest of the media in hearing a coach's view about a current NBA player, but it's something where there's a bright line in this league and you're not allowed to do it.
"And head coaches or team executives in those positions, you just say, 'I'm not permitted by the league to respond to that question.' And it's a balance of interest. I understand that. But he unfortunately crossed a bright line."
The Clippers could have $54 million in cap space to pursue free agents this summer, according to ESPN's Bobby Marks. Leonard, who is originally from the Los Angeles area, will be among the Clippers' top targets.
Johnson drew a warning from the NBA after a 2017 appearance on "Jimmy Kimmel Live" in which he made tongue-in-cheek, wink-wink-type remarks about Paul George and the Lakers. The Lakers were later fined $500,000 after an NBA investigation for tampering with George and another $50,000 when Johnson later praised Milwaukee's Giannis Antetokounmpo.