The source told The Daily Telegraph the corgis were out on a walk with the terrier, Max, at Balmoral castle in Royal Deeside, Scotland, when the animals began to fight and left Max with a torn ear and several bite wounds, The Daily Telegraph reported Monday.
The source said the dogs were with the queen's walker and no royals were present for the attack.
The attack came just days after another of Beatrice's dogs died of natural causes.
A Buckingham Palace spokesman declined to comment on the incident.
Celebrity Families of 2014 [PHOTOS]