Horford and Smart will not be in Miami for the first game of the Eastern Conference finals.
Horford is a member of the league's health and safety protocols.
Smart will not play due to his foot injury.
Ime Udoka, the coach of the team, said Monday that the veteran guard's foot was tender and sore, and that he was set to receive round-the-clock care.
Horford's absence is a significant one. He scored 30 points in a Game 4 win. He was the closest defender in the series, contesting 159 shots, the highest mark for any player in a series since Second Spectrum began tracking the stat.
Robert Williams III will be available in Boston. The center has blossomed into a huge part of Boston's team this season, playing 61 games and averaging 10 points and 9.6 rebound -- all career-highs. He missed time against Milwaukee with a bone bruise in his knee after undergoing surgery on his left knee. He was available for the game but did not play.
According to sources, Williams had a couple good days of practice and should be able to play a lot in the first game.