Animal charities have accused Prince Edward of setting a "sickening example" as pictures showed him apparently hitting his dog.
Buckingham Palace said Edward waved his stick in a bid to break up a fight between his animals over a dead pheasant at the Queen's Sandringham estate, Norfolk.
But animal rights campaigners spoke of their fury at images which they believed showed Edward apparently striking one of the dogs.
Other Royals on the shoot included Prince William, Prince Andrew and Prince Philip, it was reported.
Any person caught harming animals could face prosecution, campaigners said.
Barry Hugill, spokesman for the League Against Cruel Sports, added: "People in blood sports tend to show a complete disregard for the welfare of animals. He has set a truly sickening example."
Andrew Tyler, director of Animal Aid, added: "It is an offence to cause an animal unnecessary suffering.
"Hitting a dog is a pathetic, cowardly and vicious act - it would appear he has had a royal tantrum."
A Buckingham Palace spokesman said: "It has not been determined that he did strike the dog.
"He broke up the fight with the dogs and pictures show him waving his stick around. We cannot confirm, however, whether he struck the dog."
