Paul's injury occurred last month during Team USA training camp in Las Vegas.
The surgery was performed by hand specialist Dr. Steven Shin at the Kerlan-Jobe Orthopaedic Clinic in Los Angeles.
"(The surgery) was something we wanted him to get done now so it doesn't bother him later," Clippers coach Vinny Del Negro told the team website. "He'll be back before the start of the season."
Paul is expected to be sidelined for approximately eight weeks, which would mean he would miss most of training camp and the preseason but could return for the Clippers' opener Oct. 31 against Memphis.
Paul helped lead Team USA to the gold medal at the Olympics. He started all eight games in London, averaging 8.3 points, 5.1 assists, 2.5 steals and 25.8 minutes per game.
"Chris brought home the gold and had a terrific Olympics," Del Negro said. "He re-aggravated an injury from last season early in the (Olympic) training process and played through it."