The procedure, expected to be Thursday, will come six months after Williams had left knee surgery to repair a torn meniscus.
The latest procedure is described as a "cleanup" and is expected to allow Williams to return to full strength early in the regular season, sources said.
Williams, who will turn 25 in October, returned for the Celtics' run to the NBA Finals and played with discomfort in the playoffs that caused him to miss seven games.
Averaging 10.0 points, 9.6 rebounds and 2.2 blocks, Williams was the anchor for a Celtics team that led the league in defensive efficiency. Williams held opponents to 38.2% shooting as the closest defender, lowest among players to defend 500 shots, according to ESPN Stats & Information.
Williams also ranked second in blocked shots per game, trailing only Memphis' Jaren Jackson Jr., and shot 73.6% last season, second best among players who attempted 300 shots, according to ESPN Stats & Info.