Parliament "is going to have to consider” Andrew Mountbatten-Windsor's place in the line of royal succession, the leader of the Liberal Democrats has said.
The King’s brother is still eighth in line to the throne despite being stripped of his royal titles.
Sir Ed Davey said the monarchy will want to ensure the former prince cannot become king after his arrest on suspicion of misconduct in public office.
But an act of Parliament would be required to remove Andrew from the line of succession.
"The most important thing right now is that the police be allowed to get on with their job, acting without fear or favour," Sir Ed said on Friday.
"But clearly this is an issue that Parliament is going to have to consider when the time is right, naturally the monarchy will want to make sure he can never become king."
Detectives continued to search Andrew's former home in Berkshire on Friday, following his release from custody.
He was held on Thursday morning after allegations were made against him following the release of files related to the late paedophile financier Jeffrey Epstein.
Andrew has denied any wrongdoing over his Epstein links, but has not directly responded to the latest allegations.
Following his brother’s arrest, the King said in a statement that "the law must take its course" and the police have "our full and wholehearted support and co-operation".
Recent YouGov polling shows that 83% of Britons think the former prince should be removed from the line of succession, while just 6% believed he should not.
Various MPs and party leaders have called for a full statutory inquiry following the arrest, with some demanding a debate on the future of the monarchy.
Green Party leader Zack Polanski described the situation as "awful" and said there are many questions to be answered.
"We obviously need to wait for the legal process to make its way, but I would say we really need a full statutory inquiry into public figures from institutions, where crimes have been committed - if they've been committed - what we knew, what other people in those institutions knew and, where necessary, to make sure that the appropriate people are removed,” Mr Polanski said.
He added that he did not believe the country should have a monarchy.
"The monarchy are doing a pretty good job in themselves of not having their proudest moments over various issues we've seen in the last couple of years and, when the public are ready to have that national conversation about the monarchy, I think issues like this certainly don't help the monarchy's case,” he said.
Labour MP Richard Burgon has called for an independent inquiry into what the royal family knew about Andrew's links to Epstein.
He said: "It's time for a serious national debate about abolishing the monarchy.
"Even if you disagree, we should discuss the role of hereditary privilege in our democracy."
