Vincent, who is averaging 17.5 points a game during this series, missed Game 5 with a left ankle injury, which he suffered after landing awkwardly after taking a jump shot midway through the fourth quarter of Game 4. Vincent briefly returned to the game and was optimistic about playing in Game 5, but his ankle did not recover in time.
Kyle Lowry started in Vincent's place in Miami's 110-97 loss on Thursday. He struggled in his 30 minutes on the court, posting five points, two rebounds, one assist and four turnovers.
Martin has had a strong series off the bench for the Heat, averaging 17.6 points on 59.3% shooting from the field. He has also shot well from deep, going 14-of-31 (45.2%) on 3-pointers.
Love started the first five games of the series, averaging 5.0 points and 4.6 rebounds.
The Celtics will be without Malcolm Brogdon, the reigning Sixth Man of the Year, who has been ruled out for Game 6 with a right forearm strain.
Miami is trying to avoid becoming the first NBA team to lose a playoff series after leading 3-0.