The painting, commissioned last year as a gift for the people of Cambridgeshire, shows the pair standing side-by-side, with Kate in an emerald dress and William in a black suit.
But art critic AN Wilson says the portrait badly misses the mark.
He writes: "The Duchess of Cambridge is a life force, and this painting is dead as the dodo.
"It has reduced an animated human being to the status of a dummy; a beautiful woman to a strangely boring doll.
"The real Duchess of Cambridge cheers everyone up with her radiant smile.
"The figure in this painting is wistful, slightly petulant and actually unrecognisable as Our Kate."
He continues in his piece for the Daily Mail: "She deserves better than this frumpy, inanimate, rather sulky version of her."
The portrait was painted by award-winning artist Jamie Coreth, described as “one of Britain’s leading portrait artists” who “focuses on the character of his sitters, evoking a sense of their presence in his work" on his website.
The Duke and Duchess, both 40, met Mr Coreth as they viewed the painting of themselves on Thursday.
After looking at the painting, William said: “It’s quite big.”
He told Mr Coreth it was “amazing”.
The Duke and Duchess both studied History of Art at St Andrews University, though William later switched to Geography.
William said in a Big Issue Q&A session published this week to mark his 40th birthday: “I studied a bit of Art History at university.
“Had to give it up.
“I kept falling asleep in the lectures. Terrible.
“We did a lot of Renaissance, which was amazing.
“But then once we got into modern art, I started to get a bit dozy.”
The portrait of William and Kate was commissioned by the Cambridgeshire Royal Portrait Fund, held by the Cambridge Community Foundation, as a gift to Cambridgeshire.
The Duke and Duchess of Cambridge leave after visiting the Fitzwilliam Museum, Cambridge
Joe Giddens
The portrait of Kate and William
Jamie Coreth/Fine Art Commissions