Kensington Palace said the duchess was suffering from a severe sickness – as she did when she was pregnant with Prince George.
Speaking at a visit to Oxford University the duke said it had been a “tricky few days” but was “great news” reported BBC.
The couple’s second baby will become fourth in line to the throne, behind 13-month-old Prince George.
Asked about the duchess, Prince William said she was “feeling okay” and that he was “going to go back and look after her now”.
He told journalists the couple were “immensely thrilled”, but said it was still “early days”.
“It’s important that we all focus on the big news, the big international and domestic things that are going on at the moment. That’s what my thoughts are at the moment,” he said.
A statement from the palace said the Queen and both families were delighted with news of the pregnancy.
Prince Harry said it was “very exciting news” and joked that he “can’t wait to see my brother suffer more”.
Speaking while visiting competitors ahead of the first Invictus Games, he said Catherine was “pretty poorly” but was “doing the best she can”.
Prince William was speaking after he formally opened a £21m China study centre at Oxford University.
The duchess had been due to accompany him on the visit, but the palace said her sickness meant that she would no longer be attending and was being treated by doctors.
The duchess’s first pregnancy was revealed when she was just a few weeks pregnant with Prince George after she was admitted to hospital suffering from severe sickness in December 2012.
The sickness – called hyperemesis gravidarum – is a condition that may require supplementary hydration, medication and nutrients.
It affects 3.5 per 1,000 pregnancies, causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis.
Arriving at the new study centre at about 13:30 BST, the duke told a well-wisher who sympathised with Catherine’s condition that she may be over the worst of the acute sickness in a “few weeks’ time”.