Pierce suffered the injury in Boston's 119-114 win against Denver Friday, but played with the pain over the next two games against Charlotte and Golden State.
The team said the eight-year veteran from Kansas aggravated the injury during Wednesday's 96-95 loss to the Warriors.
An MRI exam Thursday morning revealed the damage.
He did not take part in the team's practice session and is wearing a protective boot.
"I'm a guy who has been durable my whole career," Pierce told the Boston Herald. "You never envision not playing until it happens. Just sitting around is probably going to drive me nuts. I'm glad (doctors) caught it in time."
Pierce has team-highs of 26.6 points, 4.3 assists, and 7.4 rebounds per game.
The Celtics also are without guard Wally Szczerbiak (sprained ankle) who is out indefinitely.