Brown will undergo surgery later this week, the Celtics added.
Monday's announcement comes as a surprise after Brown was forced to miss the Celtics' last three contests because of a right ankle sprain.
Before his season ended prematurely, Brown was averaging a career-high 24.7 points per outing, and he was selected to his first All-Star Game.
His injury is a major blow for a club limping toward a potential Eastern Conference play-in spot. Brad Stevens' charges sit seventh in the conference, two games back of a top-six spot and an automatic playoff berth with four games remaining.
After losing six of their last nine games, the Celtics face the Miami Heat at home on Tuesday, two days after suffering a pivotal 130-124 defeat to the Heat in Boston.