He will miss several weeks at minimum, sources told ESPN.
An MRI on Monday revealed the tear, and further evaluation during the day will help provide a timetable on a possible return. The Celtics said an update will be provided later in the week.
"There are some [operations] that keep you out longer than others," coach Ime Udoka said Monday. "We're hoping for the best."
Boston moved into first place in the Eastern Conference on Sunday, and Williams, 24, has been an immense part of a dominant league-best defense. He was injured in the 134-112 victory over the Minnesota Timberwolves on Sunday -- the Celtics' 24th victory in 28 games.
Williams is No. 1 among 169 players in the league who have defended 500-plus shots as the closest defender, per Second Spectrum tracking. Only Williams has held opponents under 40% shooting.
Williams -- who signed a new four-year, $54 million extension in the offseason -- has averaged 10 points, 9.6 rebounds and 2.2 blocks. He has shot 73% from the floor.