Thomas initially injured his hip in the third quarter of a game against the Minnesota Timberwolves on March 15, forcing the All-Star to miss the next two regular-season contests.
The 28-year-old Thomas aggravated his specific injury -- officially labeled as a right feboral-acetabular impingement with labral tear -- during Game 6 of the second-round series against the Washington Wizards on May 12.
"Isaiah has worked tirelessly to manage this injury since it first occurred," said Dr. Brian McKeon, the Celtics' chief medical officer. "The swelling increased during the first two games against Cleveland, and in order to avoid more significant long-term damage to his hip, we could no longer allow him to continue."
A femoral-acetabular impingement means that the ball joint in the hip socket is not moving freely around the cup in which it resides.
Thomas did not travel with the team to Cleveland for Game 3 on Sunday. The Cavaliers lead the series, 2-0.
Thomas, who averaged 28.9 points per game during the regular season, scored 19 total points in the first two games against Cleveland. Marcus Smart started for Thomas in the second half of Friday's 130-86 loss to the Cavaliers.