Kate is being treated by doctors at Kensington Palace for hyperemesis gravidarum, a rare condition which brings about severe vomiting during pregnancy.
It is the same illness which saw her treated in hospital in December 2012 for three nights while pregnant with Prince George.
The Duke of Cambridge said his wife experienced a “tricky few days” with very acute morning sickness, but that they are thrilled at her pregnancy.
“She’s feeling OK, thanks. It’s been a tricky few days — week or so — but obviously we’re basically thrilled, it’s great news, and early days.”
It is understood Kate’s pregnancy has not passed the 12-week stage — a similar position to when she was struck by the illness when expecting George.
Experts said she could be in for a tough time, especially as she and William have the additional pressure of having the 14-month-old toddler to look after.
Nicola James, trustee of the charity Pregnancy Sickness Support, spent five months in bed suffering from the condition when she was pregnant with her second child. “It’s highly likely that if you have had it before you will have it again, and it’s generally worse in subsequent pregnancies. It starts earlier and is usually more severe.”
Hyperemesis gravidarum can lead to dehydration, weight loss, and a build-up of toxins in the blood or urine called ketosis.
Prince Harry meanwhile, can’t wait to see his brother “suffer more”.
And asked whether he could give the new baby any “strategy” on being a younger sibling, he said: “There’s never a strategy. I think George will be over the moon. I think he will be thrilled having another small younger brother or sister.”