Kate, 42, the wife of heir to the throne Prince William, had been admitted to the private London Clinic on Tuesday where she is expected to remain for 10 to 14 days before returning home to recover, her Kensington Palace office said.
No details of the surgery were given, but a palace spokesman said the condition was non-cancerous.
"The Princess of Wales appreciates the interest this statement will generate," the statement said. "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."
Less than two hours after that unexpected announcement, Buckingham Palace revealed that Charles, 75, would also attend hospital next week for a "corrective procedure" but said his condition was benign.
"In common with thousands of men each year, the king has sought treatment for an enlarged prostate," the palace said in a statement.
The two royals have both appeared to be in good health and were last seen in public on Christmas Day when the royal family made their annual visit to a church service near King Charles' Sandringham home in eastern England.
Kensington Palace said it would only provide updates on Kate's progress when there was "significant new information to share". It added that, on medical advice, she was unlikely to return to public duties until after Easter.
William, 41, will also postpone several engagements while his wife is recovering.
Born Kate Middleton, the eldest of three children of middle-class, self-made entrepreneurs, she became the Princess of Wales after the death of Queen Elizabeth in September 2022 when William was given the title of Prince of Wales which his father had held for more than six decades.
Polls show that since her marriage to William in a grand wedding in 2011 she has become one of the most popular members of the royal family and the epitome of the modern face of the monarchy. She is also considered a global fashion icon who regularly graces the front pages of glossy magazines.
Kate and William have three children - Princes George and Louis and Princess Charlotte - and she spent four days in hospital in 2012 suffering from severe morning sickness while pregnant with eldest son George.
While few details of Kate's condition were made public, as is usual with the royals who regard medical issues as a private matter, Charles was keen to share information to encourage other men experiencing symptoms to have their conditions checked.
Britain's National Health Service (NHS) website described a benign enlarged prostate as a condition that can affect how people urinate, and is common among men over 50.
"It's not a cancer and it's not usually a serious threat to health," the NHS says on its website. "Many men worry that having an enlarged prostate means they have an increased risk of developing prostate cancer. This is not the case."
