Ramona Shelburne of ESPN first received the update from Lee's agent, Mark Bartelstein. Tom Orsborn of the San Antonio Express-News confirmed the news Saturday and noted the recovery timetable for the ailment is an estimated six-to-eight weeks.
Lee scored four points in two minutes in Game 3 of the West Finals before getting forced to exit with the knee issue. He missed Game 4 as the Warriors completed the sweep of San Antonio, which was also without stars Kawhi Leonard and Tony Parker.
The 34-year-old Florida product played a limited role for the Spurs during the team's playoff run. He averaged 4.1 points and 3.8 rebounds while playing 16.3 minutes per game across 15 appearances.
Lee provided solid per-minute contributions during the regular season, though. He ranked 15th among qualified power forwards in Player Efficiency Rating, ahead of marquee names like Paul Millsap, Kristaps Porzingis and Dirk Nowitzki, though his overall impact was smaller.
In April, the two-time All-Star selection told Orsborn he wasn't sure what the future held, but he enjoyed his first season in San Antonio.
"It's been a great fit overall," he said. "That's the best way to put it."
Lee's current contract includes a player option for the 2017-18 NBA season. He can either accept a $1.6 million salary to stick with the Spurs or decline to become an unrestricted free agent.
The timeline for his recovery from the knee injury means he should be ready for the start of training camp, which is usually in late September, barring any setbacks.