The cause of the dog's death was not reported.
Monty, 13, and two other corgis were seen greeting James Bond actor Daniel Craig before he accepts a mission from the queen in the short film, the BBC reported Saturday.
The three dogs ran down the stairs in Buckingham Palace ahead of the queen and Craig and performed tummy rolls.
Buckingham Palace officials also announced the death of Cider, one of the Queen's dorgis, a dachshund-corgi cross-bread.
The death of Monty and Cider leaves two remaining corgis at the palace -- Willow and Holly -- in addition to two dorgis, Candy and Vulcan.
The tradition of corgis in the British royal family dates back to 1933 when the future King George VI bought his first Pembroke Corgi.
Monty was named after Monty Roberts, who advises the Queen on horses and corgis. Roberts, 77, has offered to give the Queen a corgi puppy to carry on the tradition, The Mirror reported.