John Healey said his department was “working to remove” the rank, which Andrew was awarded on his 55th birthday in 2015.
The rank is his last remaining honorary military title since he handed back the others in 2022 over his connections with the paedophile financier Jeffrey Epstein.
Mr Healey said: “In general, the Government’s been guided by the decisions and judgments King Charles has made.
“In defence, it’s exactly the same. And we’ve seen Andrew surrender the honorary positions he’s had throughout the military, and guided again by the King, we are working now to remove that last remaining title of vice-admiral that he has.”
Defence Secretary John Healey(Jeff Moore/PA)
The British Defence Secretary would not comment on whether Andrew would be able to keep his medals, including the campaign medal he received for his service in the Falklands War, but said the Ministry of Defence would be “guided by the decisions the King makes”.
The move follows King Charles’ decision to strip his brother of his peerages and the title of prince on Thursday amid the continuing fallout of the Epstein scandal.
Andrew’s Duke of York title has already been removed from the Roll of Peerages.
Andrew has been associated with the Royal Navy since 1979, when he began officer training at Britannia Royal Naval College in Dartmouth.
He subsequently served as a helicopter pilot and was part of the task force deployed to retake the Falklands following the Argentinian invasion in 1982.
He ended his active naval career in 2001 with the rank of commander, but later received honorary promotions including to vice-admiral in 2015.
Meanwhile, it has been claimed that Andrew routinely refused to sign off statements that supported survivors of abuse connected to Epstein.
Charles and the Queen of England publicly shared their “thoughts and utmost sympathies” with “the victims and survivors of any and all forms of abuse” as part of the announcement.
A friend of King Charles and Camilla told The Sunday Times that references to victims were removed from all previous statements drafted by courtiers and issued by Buckingham Palace since Andrew’s disastrous Newsnight interview in 2019.
Any such communication had required Andrew’s sign-off, the paper said.
The former prince denies sexually assaulting the late Virginia Giuffre, who alleged this happened on three occasions, including when she was 17, after being trafficked by Epstein.
The friend told the paper that King Charles had “lost patience” and his statement announcing the removal of Andrew’s prince and Duke of York titles was “no longer a statement by committee, it’s a statement from the King”.
Buckingham Palace declined to comment.
Pressure is also building on Andrew to give evidence before a powerful US Congressional committee.
Members of the House Oversight Committee have called for the former prince to reveal what he knew about the actions of Epstein.