The surprise move from the 92-year-old Australian billionaire leaves his son Lachlan firmly in line of succession at Fox and the rest of the media empire.
Murdoch will become chairman emeritus of both the news network's parent company, Fox Corp, and the News Corp media holdings while Lachlan will become News Corp chairman and continue as chief executive officer of Fox Corp, effective in November.
"(Murdoch has) built a vast global media empire, and no doubt the business pages will give him credit for that, but he has done enormous damage to the democratic world," Mr Turnbull told ABC News .
"The anger-tainment ecosystem that Fox News, above all, has created in the US has left America angrier and more divided than it's been at any time since the civil war.
"Murdoch has been the largest voice in the English-speaking world - or the loudest voice, at any rate - to deny the reality of global warming and delay action to address it ... so, it's a hell of a legacy, I have to say."
The former prime minister did not believe much would change with Lachlan taking the helm.
"Rupert has always been fascinated by power - he's drawn to it like a moth is to a flame - and so he's enjoyed exerting the power that he has over the political system," he said.
"I think Lachlan is, if anything, more ideological than his father so I don't think there's going to be any change for the better, that's for sure."
Treasurer Jim Chalmers was more tempered in his reaction, describing Murdoch senior as one of the defining figures of the global media landscape.
"He's a controversial figure, but also an influential figure," Dr Chalmers told ABC Radio.
"In lots of ways it's the end of an era at News, and there will be mixed views often strongly held about his contribution."
Foreign Minister Penny Wong reflected on Murdoch's influence in Australian politics.
"Any fair-minded observer might say that some of the News Limited papers might not exactly be cheerleaders of the Labor Party, but that's what happens in a democracy," she said.
"And I wish him well for his retirement."