The Princess of Wales, 42, underwent a successful operation at a private hospital in London on Tuesday.
Kensington Palace said she will remain there for ten to 14 days and is “unlikely” to return to public duties until after Easter.
The statement read: “The Princess of Wales wishes to apologise to all those concerned for the fact that she has to postpone her upcoming engagements.
“She looks forward to reinstating as many as possible, as soon as possible.”
The palace said the public “will understand her desire to maintain as much normality for her children as possible”.
It was earlier confirmed the operation was planned and it is not to do with Cancer.
Updates on her recovery will come when there are only “significant information to share”, a spokesperson said.
Kate is now expected to miss out on a string of engagements including the BAFTA’s on February 18 and St David’s Day parade March 1.
The mum-of-three is also expected to be absent from the St Patrick’s Day parade on March 17 and Church on Easter Sunday.
She may miss Prince Edward’s 60th birthday celebrations on March 10.
In the statement issued on Wednesday afternoon, Kensington Palace said: “Her Royal Highness The Princess of Wales was admitted to The London Clinic yesterday for planned abdominal surgery.
“The surgery was successful and it is expected that she will remain in hospital for ten to fourteen days, before returning home to continue her recovery.”
A spokesperson added: “The Princess of Wales appreciates the interest this statement will generate.
“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.”
The London Clinic, near Regent’s Park in central London, describes itself as the UK’s largest independent private hospital.