Norman Baker, who served under Theresa May in the coalition government, also said police time should be “used solve crime rather than to massage royal egos”.
The Liberal Democrat former MP said the £2m cost of keeping order at the ceremony in Windsor was “outrageous”, adding: “No other country with a monarchy would put up with this.”
The cost of policing the celebration, which includes a carriage ride by Eugenie and her groom, the drinks executive Jack Brooksbank, currently falls to the taxpayer.
Eugenie is the Queen’s granddaughter and ninth in line to the throne. She will walk down the aisle in St George’s Chapel inside Windsor Castle – as the Duchess of Sussex had done earlier in the year – in front of more than 800 guests.
Security arrangements take into account the large number of senior Royals in attendance the ceremony, as well as the carriage procession.
Mr Baker said: “It is outrageous that the taxpayer is to be handed a £2m bill for security costs, just so some nonentity royal can have an ego trip in a carriage through the streets.
“Prince Andrew, who is not short of cash, should refund the taxpayer the cost of the wholly unnecessary security bill.”
Mr Baker, a former crime prevention minister, resigned from the Home Office in 2014 and was fiercely critical of Mrs May’s performance as Home Secretary.
He lost his seat at the 2015 election and has since spent nine months as managing director of a bus operator in Brighton called The Big Lemon.
Meanwhile, rough sleepers are being advised to “consider avoiding” parts of Windsor town centre during the wedding.
The Royal Borough of Windsor and Maidenhead council said it was telling homeless people to anticipate “higher footfall” in the area when festivities take place.
The council faced a backlash over plans to clear rough sleepers from the streets ahead of Harry and Meghan’s wedding in May and the proposals were eventually dropped.
This time, it said it was not asking homeless people to vacate the area. A spokesman said sleepers were being advised that “due to their vulnerability they may want to move locations within the town centre”.
The council added it would offer “safe storage of certain posessions”.
Buckingham Palace has declined to comment.