The 6-foot-11 inch Garnett was injured while attempting a slam in the closing minutes of the first half of a 90-85 Thursday loss to the Utah Jazz in Salt Lake City.
Garnett limped off the court, but subsequently was helped into the locker room and did not play in the second half.
Danny Ainge, Boston's executive director of basketball operations, told ESPN NBA analyst Jackie MacMullan that Garnett will stay in Boston for the remaining three games of the Celtics' West Coast trip.
"I'd rather have him healthy for the playoffs, that's how I look at it," Coach Doc Rivers said after the loss to Utah.
Boston plays at Phoenix Sunday, Denver Monday and Los Angeles against the Clippers on Wednesday.
Garnett has averaged 16.3 points and 8.8 rebounds in 53 games this season.