The bisexual contestant altered the lyrics of 'And I Am Telling You' by Jennifer Hudson so that he was singing about a woman, rather than a man.
Minogue stated: "If you're to believe everything you read in the papers, then you didn't need to change the gender references in the song."
The 37-year-old's remark was met with outrage by Johnson's mentor Simon Cowell, who replied: "You can forget playing any of those games with him. I'm not having that. This guy sang his heart out. Give him some credit."
An X Factor statement on Minogue's official blog explained that the judge had not meant to cause offence.
It read: "Dannii is mortified if her comments have been misinterpreted as she has always been hugely supportive of the gay and bisexual community for her entire career."
The statement also revealed that Minogue had spoken to Danyl after the show and that Johnson did not have a problem with her comment.
The X Factor continues tonight at 8pm on ITV1.