The man formerly known as Prince Andrew was taken into police custody on Thursday night (AEDT) and questioned on suspicion of misconduct in public office - an offence in the UK which carries a maximum sentence of life in prison.
He was then later released pending further investigation.
The police probe relates to allegations he leaked sensitive documents to dead paedophile financier Jeffrey Epstein while serving as the UK's trade envoy in 2010.
Prime Minister Anthony Albanese said it was extraordinary to see a man who once led a life of absolute power and privilege placed under arrest.
"This appears to be about (classified) documents, and whether they were inappropriately forwarded on to someone who wasn't eligible," he told the Guardian's Australian Politics podcast.
"But, of course, there's the bigger issue as well when it comes to Andrew Mountbatten-Windsor."
Asked about whether he was planning a referendum for Australia to leave the monarchy and become a republic, Mr Albanese said he wasn't.
"I'm a republican but we had a referendum during the last term. Referendums are hard to pass in Australia," he said.
Opposition Leader Angus Taylor said Mountbatten-Windsor needed to answer to the courts, but wouldn't be drawn when asked whether it was time to remove him from the line of succession to be Australia's head of state.
"I think the issue you raised is one that will come up over time, I'm sure, but right now, I think the important point to make is that we're all equal before the law," he told reporters in Melbourne.
The disgraced 66-year-old is still eighth in line for the British throne.
The family of Virginia Roberts Giuffre, an Australian-American woman who alleged she was sexually abused by Mountbatten-Windsor and Epstein as a teenager, said they were grateful to police for the arrest.
"Today, our broken hearts have been lifted at the news that no one is above the law, not even royalty," Sky Roberts, Amanda Roberts, Danny Wilson and Lanette Wilson said in a joint statement.
"(Andrew) was never a prince. For survivors everywhere, Virginia did this for you," they said.
Ms Giuffre died by suicide at her home in Western Australia in 2025.
Mountbatten-Windsor has always denied the allegations against him.
Health Minister Mark Butler said the law now needed to follow its course.
"What a fall from grace," he told Seven's Sunrise program.
"A man we knew for decades as Prince Andrew, His Royal Highness, is now just a man in his 60s from Norfolk."
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