Heat coach Erik Spoelstra said both would sit out Monday's game against the Washington Wizards.
The Heat have been competing with the Indiana Pacers for the No. 1 seed in the Eastern Conference, but Pacers trimmed their magic number to one with a win over Oklahoma City Thunder on Sunday.
Spoelstra said James is "dealing with some minor ailments" but "nothing that's significant enough that will keep him out" for the playoffs. He said the same was true for Bosh.
Dwyane Wade, who recently returned from a hamstring injury, was expected to play.
The Heat wrap up their season Wednesday against the Philadelphia 76ers.