The Princess was admitted on Tuesday for the planned procedure but is expected to stay in the clinic for 10 to 14 days before returning to her Adelaide Cottage home in Windsor.
The nature of her condition has not been revealed, although Kensington Palace confirmed that it was not cancerous.
It is serious enough, however, for the heir to the throne to be postponing official duties while his wife is in hospital and in the immediate aftermath while she recuperates, devoting his time to his family.
The Princess is not expected to return to public duties until after Easter, but this will depend on medical advice at the time.
