It is understood that Kate's pregnancy has not passed the 12-week stage - a similar position to when she was struck by the illness when in the early stages of her first pregnancy.
A Kensington Palace spokesman said the Duchess's attendance at future events would be decided on a 'case by case' basis.
Kate is scheduled to be among the guests at the opening ceremony of the Invictus Games in London on Wednesday evening along with William, Harry and the Prince of Wales and Duchess of Cornwall.
The Royal Navy in Portsmouth took part in traditional celebrations to signify the birth of Prince George.
Around 600 sailors took part as they 'spliced the mainbrace' - a centuries-old tradition where rum is drunk.
In a signal to Navy personnel across the globe, First Sea Lord Admiral Sir George Zambellas said: “I recently had the pleasure of sending loyal greetings and warmest good wishes, on behalf of the Royal Navy, to Her Majesty The Queen on the birth of HRH Prince George of Cambridge."
Splicing the mainbrace came from when sailors had to fix the main brace of a sail that had broken in storm or battle. The sailor who carried out the task was rewarded with an extra ration of rum.
However, now the saying refers to a special occasion such as a change of monarch, royal birth or royal wedding.
A Dorset company has been left out of pocket after it ordered commemorative plates marking the birth of a Royal Princess.
After the birth of Prince George of Cambridge the company is ruing the fact it now has 5,000 pink plates commemorating the arrival of a “Royal Princess”.
The Daily Telegraph is reporting that the company, which has not been named, received an “inside tip” from a supposedly reputable source who insisted the baby was a girl.
The little prince has a name! The Duke and Duchess of Cambridge have announced that he will be called George Alexander Louis.
The baby will be known as His Royal Highness Prince George of Cambridge
The little prince has got a name! The Duke and Duchess of Cambridge have announced that he will be called George Alexander Louis.
First pictures of the vehicles carrying the Royal baby and his parents arriving in Bucklebury.
WIlliam and Kate, along with the new arrival, leave Kensington Palace on their way to the Middleton family home in Bucklebury.
William and Kate have arrived home in Bucklebury with their new son. More shortly.