Marc J. Spears of ESPN reported Joel Anthony had to replace Lee on free-throw attempts before the forward was ruled out for the rest of the game.
Ramona Shelburne of ESPN noted Lee will have a MRI on Sunday.
This is a difficult setback for Lee, who played only 55 games last season and 49 in the prior campaign. He had 7.3 points and 5.6 rebounds per game in 2016-17.
The veteran, who has been in the league since 2005, played for the New York Knicks, Golden State Warriors, Boston Celtics and Dallas Mavericks before joining the Spurs. While he is past his prime, the two-time All-Star earned third-team All-NBA honors in 2012-13.
The 34-year-old has eight seasons with double-digit scoring figures and four with double-digit rebounding averages and has been a solid role player for this season's deep Spurs team.
San Antonio has LaMarcus Aldridge and Pau Gasol to shoulder the load until Lee is ready to return. Aldridge can control the glass and score 25 points on any given night, while Gasol is likely a future Hall of Famer with a championship pedigree. The Spurs also have Dewayne Dedmon for depth purposes.