Hayward, who signed a four-year, $120 million contract to join Charlotte as a free agent in November, was set to make his return to Boston for the first time since leaving the Celtics in the offseason before he suffered the injury during Friday's 114-97 win at Indiana.
He will be reevaluated in about four weeks, the team said.
Embracing a bigger role in Charlotte than he had in Boston, Hayward has excelled for the Hornets this season, averaging 19.6 points, 5.9 rebounds and 4.1 assists per game while shooting 41.5% from 3-point range.
The Hornets -- already without star rookie LaMelo Ball, who is out indefinitely with a fractured wrist -- have been one of the league's biggest surprises this season. Heading into Sunday's game in Boston, Charlotte sits two games over .500 and in fourth place in the Eastern Conference.
The Hornets enter Saturday night's action projected by ESPN's Basketball Power Index to finish sixth in the East, which would allow them to avoid the play-in tournament and make the playoffs for the first time since losing in seven games to the Miami Heat in the first round of the 2016 playoffs.
Since returning to the league as an expansion team for the 2004-05 season, Charlotte has made the playoffs only three times and has yet to advance out of the first round.
The Hornets are 1-3 in the four games Hayward has missed this season (24-20 with him), allowing 9.5 points per game more than when Hayward plays, according to ESPN Stats & Information data.