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It means the second-placed Heat will be without their two biggest weapons - McCullum and Chris Lynn, who is with the Australian ODI side - for Tuesday's crucial game against the Melbourne Stars.
Queensland Cricket chief executive Max Walters said it was disappointing to lose the former New Zealand test captain, given how well fans have received the Heat's exciting and attacking brand of play.
However, after reviewing the match, the Heat determined there were no grounds for an appeal and accepted the penalty.
"It is a shame but we accept those are the competition rules we are playing under and reminds us that we can continue to improve in all facets of the game," Walters said.
Joe Burns will step in as captain while McCullum serves his ban, which was handed down today for a second breach of the playing conditions this season.
Each member of the Heat team has also been fined $500.
The side initially copped $1000 a player but that was downgraded because they didn't appeal the penalty.
It came after the Heat were six minutes behind the scheduled time to complete their 20 overs during Wednesday night's Gabba loss to the Perth Scorchers, which allowed the Scorchers to supplant them atop the BBL ladder.