The photographs were said to show Kate peeling off her bikini top by the swimming pool while in conversation with her husband.
William and Kate had been staying at a chateau owned by Viscount Linley, the Queen's nephew.
Aides travelling with the royal couple in South East Asia were informed at 5am local time about the release of the images. They broke the news to the Duke and Duchess before their visit to a mosque in Kuala Lumpur.
Palace officials are expected to contact lawyers in France and will consider all options available to them once they have verified that the pictures are genuine.
Despite the incident the couple put on a brave face, smiling their way through the visit on Friday, like the united team they have become.
Royal aides said the couple are "furious" and the future King was particularly upset about the invasion of his wife's privacy.
"The incident is reminiscent of the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales, and all the more upsetting to The Duke and Duchess for being so," said a palace statement.
"Their Royal Highnesses had every expectation of privacy in the remote house. It is unthinkable that anyone should take such photographs, let alone publish them."
It added: "The Duke and Duchess remain focused currently on their Tour of Singapore, Malaysia, Solomon Islands and Tuvalu on behalf of HM The Queen."