Dutton admitted that he sent the text after reading a column written by Samantha Maiden, political editor for News Corp’s Sunday newspapers.
“I apologised to her straight away which she took in good faith,” the minister said in a statement late Sunday.
“Sam and I have exchanged some robust language over the years, so we had a laugh after this.”
Maiden said Monday she was not offended despite reports the message included some very strong language.
News Corp’s Daily Telegraph called the SMS text “blistering”.
“Certainly, he did call me a mad witch, that much is true,” she told the Australian Broadcasting Corporation.
“I was more than happy to accept Peter Dutton’s apology.
“As soon as he sent me that text saying ‘Mate, she’s a bit of a mad witch’ I sent him a text saying ‘Mate, you’ve sent the text to the mad witch’.
“Bit of a rookie error,” Maiden said, adding that Dutton should not be stripped of his portfolio.
The message was reportedly intended for the former cities and built environment minister Jamie Briggs in response to her coverage of his resignation last Tuesday.
Briggs confessed to an “error of professional judgement” in a Hong Kong bar with a female public servant.
Media reports said he put his arm around a young consulate staffer and kissed her on the cheek.
Dutton was also in hot water last September when a microphone picked up his attempted joke to then prime minister Tony Abbott about time-keeping on Pacific islands and the threat of sea flooding due to climate change.
“Time does not mean anything when you are about to have water lapping at your door,” Dutton quipped, before being told a microphone was still on.