The specifics of the allegations of misconduct in public office against Mountbatten-Windsor remain unclear, but they do not relate to any sexual offences.
Police in the UK said they were assessing a complaint over the alleged sharing of confidential material by the former prince with Epstein.
Mountbatten-Windsor is among a long list of high-profile names included in the Epstein files released by the justice department, including Elon Musk, Bill Gates, US President Donald Trump, former US President Bill Clinton, Richard Branson, Peter Mandelson and Sarah Ferguson.
Many people whose names were included in the document have denied wrongdoing, and being named in the files does not imply criminal activity.
But US lawmakers have said they are committed to continuing their investigation, regardless.
“No one connected to Jeffrey Epstein will escape accountability for their crimes,” Democrats on the House Oversight Committee wrote on social media after Mountbatten-Windsor’s arrest.
“Our work is just beginning, and we will pursue justice for every individual who participated in the abuse of women and girls.”
Subramanyam and fellow congressman Robert Garcia previously requested Lord Mandelson, the former British Ambassador to the US, to sit for a deposition regarding his relationship with Epstein.
On Thursday, Garcia said that request had been denied because Lord Mandelson’s lawyers said “he is unable to appear due to the ongoing investigation by the Metropolitan Police”.