Minogue made a comment on Saturday night's show after Johnson changed the lyrics of the Jennifer Hudson song, 'And I Am Telling You'.
The former pop singer made reference to a story in the News of the World, which alleged that Johnson is bisexual.
Minogue said: "If we're to believe what we read in the papers, there was no need to switch the gender reference in that song."
Johnson appeared shocked by the comment and fell silent, while Minogue's fellow judge Simon Cowell shot her an angry look, although frequent viewers of the show will note there is nothing unusual about this.
Ofcom has logged 3,885 complaints so far, despite Minogue's repeated apologies, most of which complain that the comment was offensive.
An Ofcom spokeswoman said the media regulator had no plans at present to investigate the complaints, but could not yet reveal its reasoning due to procedural guidelines.
After her comment made headlines, Minogue protested that Johnson was "an openly bisexual guy".
She explained: "It was meant to be a humorous moment about the fact he had an opportunity to have fun with his song.
"Danyl and I were joking about the very same thing in rehearsals on Friday, so it carried on to the show.
"I'd like to apologise to anyone that was offended by my comments, it was never my intention."
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