The 66-year-old was taken into police custody on Thursday night (AEDT) on suspicion of misconduct in public office, before being released.
Despite being stripped of his titles, Mountbatten-Windsor remains in the line of succession to the British throne, meaning he is also eighth in line to be Australia's head of state.
Asked about the arrest on Friday morning, Health Minister Mark Butler said the law 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."
Mr Butler said his thoughts were with the girls and women caught up in the "hideous network of powerful men" organised by dead pedophile financier Jeffrey Epstein.
UK police are investigating allegations Mountbatten-Windsor shared confidential documents with Epstein while serving as the country's trade envoy in 2010.
He has also been accused of sexually abusing then-17-year-old Virginia Giuffre, and reached an undisclosed settlement with her in 2022 but has always denied the claims.
Deputy Opposition Leader Jane Hume said the former prince - who was stripped of his titles in late 2025 over the allegations - was accused of serious offences.Â
"This is an extremely disturbing fall from grace," she told Sunrise.
"The misconduct in public office is a very serious allegation. We should let the full course of the law take its place, but it's also a reminder that nobody is above the law," Senator Hume said.
Independent MP Dai Le said it was "shocking" to see the former prince in police custody, while Labor party president and former federal treasurer Wayne Swan said it was important the rich and powerful were held to account.
"I think in society these days, there's a suspicion that that the powerful and the rich get away with a lot and everyone else can please themselves," he told Nine's Today Show.
"So I think many people will be surprised with this turn of events," Mr Swan said.
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