The palace said the surgery on Tuesday was successful and the former Kate Middleton, 42, is expected to remain in the hospital for 10-14 days before returning home.
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It is unlikely she will return to public duties until after Easter.
The palace said that Kate, the wife of Prince William, wished to apologize for postponing her upcoming engagements.
"The Princess of Wales appreciates the interest this statement will generate," the palace said in a statement. "She hopes that the public will understand her desire to maintain as much normality for her children as possible; and her wish that her personal medical information remains private."
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Because of that request, officials said they will only provide updates to the public on her progress when there is significant information to share.
A royal by choice - not birth - Kate is the daughter of a flight attendant and a flight dispatcher. Born in Reading, England, on Jan. 9, 1982, Catherine Elizabeth Middleton grew up with a younger sister, Pippa, and a younger brother, James.
The family is from a well-to-do area of Berkshire, west of London, and moved to Jordan when Kate was 2 years old because of her father's work. They returned to England in 1986, and Kate attended the exclusive Marlborough College, where she was active in sports such as tennis.
She first met met Prince William, the elder son of the late Princess Diana and King Charles III, at the University of St. Andrews in Scotland.
After Prince Harry and Meghan's stormy departure to California in 2020, the Prince and Princess of Wales have solidified their position as being among the most popular members of the royal family. Kate, in particular, has remained a reliable royal in the public eye - the smiling mother of three who can comfort grieving parents at a children's hospice or wow the nation by playing piano during a televised Christmas concert.
She was among the royals who appeared at the annual Christmas Day service at Sandringham.
(The Associated Press contributed to this report.)