The recovery process is expected to take nine months, leaving Beverley with the expectation of a full recovery to return next season. He underwent the procedure in Houston.
The loss of Beverley leaves the Clippers (6-11), who ended a nine-game losing streak Wednesday, without their opening-night starting backcourt for an extended period. Guard Milos Teodosic, a 30-year-old European rookie, has missed most of the regular season with left plantar fasciitis. He isn't expected back soon.
"It's a tough blow for the team, but it's worse for Patrick,'' Clippers coach Doc Rivers told reporters in Atlanta before his team went out and beat the Hawks 116-101. "We thought it would probably be just meniscus, but it turns out to be a lot more."
The Clippers are using veteran guards Austin Rivers, Lou Williams and rookie Sindarius Thornwell in increased roles. The team has a roster spot available, but the Clippers are only $122,000 below the luxury tax and $6.1 million below the hard cap. Los Angeles is eligible to apply for the Disabled Player Exception valued at $2.75 million.
Beverley, whose $5 million contract in 2018-19 is non-guaranteed, had missed five straight games with a sore right knee before returning to play 22 minutes in the Clippers' 107-85 loss to the New York Knicks on Monday.
Beverley had averaged 12.9 points, three assists and three rebounds for the Clippers this season.
"He's a guy that you just want around your team as much as possible, and the fact that he won't be hurts our team for sure," Rivers said.
The Clippers have won only once since their buzzer-beating victory over Portland on Oct. 29 that started their season 4-0.
Information from ESPN's Bobby Marks was used in this report.