The Duke, 59, and Duchess of York, 59, took a private jet to the Costa del Sol on Wednesday afternoon and are believed to have travelled to the Spanish retreat of Sotogrande.
The American billionaire financier Epstein, 66, was found unresponsive in his New York jail cell on Saturday, while awaiting trial on charges of sex trafficking.
He was later pronounced dead at a hospital in an apparent suicide.
The two thousand pages of previously sealed court documents released last Friday focused on testimony by a woman who claimed she was Epstein's "sex slave."
Virginia Giuffre, now 35, claimed she was forced to have sex with well-known American political and business personalities. They have all denied the allegations.
The newly released legal documents also included previous allegations about Prince Andrew.
A Buckingham Palace spokeswoman said: "This relates to proceedings in the United States, to which the Duke of York is not a party.
“Any suggestion of impropriety with underage minors is categorically untrue."
A source told The Sun: “The Duchess insisted she go on holiday with the Duke to look after him and show the world she stands by him.
“She feels this is like the old days when they would take on the world together. She knows she has to get him away from all the headlines.”
The Duke of York attended church with his mother the Queen last weekend in Balmoral, Scotland.
Fergie also planned to spend the week with him and their daughters Princess Beatrice, 31, and Princess Eugenie, 29, but she was ‘forced to leave Balmoral’ after the Duke of Edinburgh arrived for his summer holiday earlier than planned, according to reports.
Andrew and Fergie have remained on good terms, despite divorcing in 1996.