The statement said Catherine was in the King Edward VII Hospital in Central London suffering from very acute morning sickness. She is likely to remain there for several days.
It said her condition required supplementary hydration and nutrients. There was no detail about when the baby was due, with the statement stating the pregnancy was in its early stages.
“I'm delighted by the news that the Duke and Duchess of Cambridge are expecting a baby,” Prime Minister David Cameron said on his Twitter website. “They will make wonderful parents.”