With little of the usual royal pomp and fanfare, the 31-year-old Beatrice married property developer Edoardo Mapelli Mozzi on Friday at Windsor Castle.
She is the eldest daughter of Prince Andrew and Sarah, Duchess of York.
The couple had originally planned to marry in May, but the coronavirus lockdown forced them to reschedule and have a low-key ceremony.
The 94-year-old monarch and her husband Prince Philip (99) were among the few who attended. Wedding ceremonies have been allowed in England since July 4 but with a limit of 30 guests.
"The couple decided to hold a small private ceremony with their parents and siblings following the postponement of their wedding in May," the palace said in a statement.
Maxwell is charged with luring young girls for late US financier Jeffrey Epstein to sexually abuse, accusations she denies.
US prosecutors also want to question the British prince about his contacts with Epstein but say he has so far evaded their requests, an allegation he rejects.
Buckingham Palace said Beatrice, who is ninth in line to the throne, wore a vintage ivory dress by Norman Hartnell and the Queen Mary diamond fringe tiara, both loaned to her for the day by the Queen.
Elizabeth wore the same tiara, made in 1919 from a diamond necklace given to Queen Victoria for her wedding, when she married Philip in 1947.
"Working within government guidelines, the service was in keeping with the unique circumstances while enabling them to celebrate their wedding with their closest family," the palace said.
"No hymns were sung, but a selection of music was played. The National Anthem was played but not sung."
The groom (37) has a young son called Wolfie from a previous relationship.
Beatrice's sister, Princess Eugenie, married her long-term partner Jack Brooksbank at Windsor Castle in October 2018.
