The Australian Broadcasting Corp (ABC) was criticised after a former terror suspect was allowed on live television show Q&A two weeks ago.
Agriculture Minister Barnaby Joyce has cancelled his Monday night appearance, according to local media reports.
Mr Joyce's office cited the prime minister's order for why he cancelled his appearance, local media said.
"The Prime Minister has communicated that he does not want any frontbencher to appear on Q&A," a spokesman for Mr Joyce told the Sydney Morning Herald.
The Q&A program has become a lightning rod for debate in Australia about national security and freedom of speech.
The ABC last week conceded it was wrong to let Sydney man Zaky Mallah appear live on the programme to ask a question.
It is undertaking a review of the decision.
In 2005, Mallah was convicted of threatening to kill government officers but acquitted of terrorism charges.
From his position in the Q&A audience, he confronted Parliamentary Secretary for Foreign Affairs Steven Ciobo about the government's plans to strip dual nationals of citizenship if they supported terrorism.
Mr Ciobo, who was a panel guest, told Mallah he was pleased to be part of a government "that would say that you were out of the country".
Mallah angrily replied the government had "just justified to many Australian Muslims in the community tonight to leave and go to Syria and join [Islamic State] because of ministers like him".
The ABC show allows audience members to put questions to a panel of figures from various sides of Australian political and social life. High-profile politicians regularly appear on it.
Mr Joyce had said on Sunday he would be appearing on Q&A, before being told not to.
Speaking on Monday at a National Press Club address, Mr Joyce said "no threat was made" by Mr Abbott's office, but it would have been nice to have received more notice.
"That's life, you take it on the chin, he said, adding that Mr Abbott did not want ministers appearing on the show until the ABC's own review had been completed.
After Mallah appeared on the programme Mr Abbott said "heads should roll" and questioned the ABC's allegiance.
A self-styled media critic and Muslim activist, Mallah had previously been interviewed by several major Australian media outlets and international broadcasters, including the BBC.
More recently, his regular social media posts have attracted criticism, in part, because of crude and sexist references to several female journalists.
A government review led by the Department of Communications found the producers were aware of his criminal convictions but not his more-recent derogatory social media posts when he was selected to ask a question.
The Australian Prime Minister has told his cabinet to boycott a popular talk show on the national broadcaster.