Regiments of the Queen's Guards including the Scots Guards and the Coldstream Guards wear bearskin hats, made from the North American black bear.
Stone, 23, is seen holding a teddy bear that covers up most of her naked body, with the slogan "Bear Hugs, Not Bear Caps" in the background.
"Too many people at the Ministry of Defence are dragging their heels on this issue, and I feel like more needs to be done to stop the murder," the Daily Mail quoted Stone as saying.
"It's time for the Ministry of Defence to finally make the switch and go fur-free, and I hope that the ad I have created with PETA helps raise awareness and puts a stop to this unnecessary killing," she added.
Animal welfare group PETA are campaigning against the killing of the bears for the hats, but a MoD spokesperson has defended the military's decision to kill bears.
"The North American Black Bear, whose fur is used, are not killed specifically for the Footguards caps," the spokesperson said.
"Their numbers in the USA and Canada are kept under control through very strictly enforced licensing regimes - this is how the fur is sourced.
"We have looked into alternative man made materials in the past, but none has come remotely close to matching the natural properties that bear fur possesses.
"We would be very happy to work with any potential supplier who believes they have the answer," the spokesperson added. (ANI)