Coach Erik Spoelstra said the decision, announced less than two hours before tipoff, was "somewhat close.''
Replacing him in the lineup was center Greg Oden, who made his first NBA start since December 2009.
James has been in top form lately, scoring at least 33 points in each of the past four games, all wins. But he had no problem with the decision, Spoelstra said.
"He didn't stand up and put up his dukes and fight us,'' the coach said. "We still understand the big picture. The fact that we don't play until Thursday, it makes the most sense.''
James broke his nose midway through the fourth quarter of Thursday's victory at Oklahoma City and sat out the rest of the game. His nose was reset by a doctor Friday and he missed practice Saturday.
Even if James returns for the Heat's home game Thursday against the New York Knicks, he'll get a week off -- a rare idle stretch for one of the NBA's most durable stars.
"It doesn't hurt at all,'' teammate Dwyane Wade said. "When you're in such a great rhythm, you don't want anything to stop that. But at the same time, to get this time off to regroup, when he comes back on the court -- hopefully Thursday -- he'll feel a little fresher. That'll take him to the end of the season for sure. He doesn't need much.''
The only other game James missed this season was in December, when he sat out because of a groin injury while the Heat won at Portland.
Meanwhile, Bulls swingman Jimmy Butler will miss Sunday's game because of sore ribs. Butler left Friday night's win over the Denver Nuggets after a collision late in the first quarter and never returned to the game.
Butler said he is day to day and hopeful to be back on the floor on Tuesday night against the Atlanta Hawks. He reiterated that there is not a break, just a bruise.
ESPNChicago.com's Nick Friedell and The Associated Press contributed to this report.