Davis suffered the injury while setting a screen during practice. He is expected to miss two weeks.
"We're going to take our time with that," Clippers coach Doc Rivers said. "I don't give a time frame, but no time soon ... I think it will be close [to the season opener]. I think he'll be back playing by then, but I don't know if he'll be in basketball shape to play."
Davis played in 23 regular-season games with the Clippers last season, averaging 4.2 points and three rebounds in 13.4 minutes per game. He averaged 3.8 points and 2.8 rebounds in 12.2 minutes per game during the postseason.