The video, obtained by The Sun, appears to show a masked figure in a dark hoodie holding a crossbow and addressing the camera with a distorted voice, saying they wanted to "assassinate the Queen" in a "revenge" mission.
It comes after a 19-year-old man was arrested on Christmas Day within the grounds of the castle in Berkshire where the Queen is in residence.
The man, from Southampton, was arrested on suspicion of breach or trespass of a protected site and possession of an offensive weapon.
Police said he has since been sectioned under the Mental Health Act and remains in the care of medical professionals.
A spokesperson from Scotland Yard said: "Security processes were triggered within moments of the man entering the grounds and he did not enter any buildings.
"Following a search of the man, a crossbow was recovered."
They added: "Inquiries into the full circumstances of this incident are being progressed by Metropolitan Police specialist operations."
The Met would not comment on who appeared in the video, but a spokesperson said in a statement: "Following the man's arrest, detectives are assessing the contents of a video."
A Buckingham Palace spokeswoman declined to comment.
The Queen spent Christmas Day at Windsor Castle and was expected to have lunch with the Prince of Wales and the Duchess of Cornwall, and the Earl and Countess of Wessex.
Charles, Camilla, Edward and Sophie, the latter couple along with their children Lady Louise and James, Viscount Severn, attended a church service in St George's Chapel, in the castle grounds, at 10.45am on Christmas morning.
In May, Thames Valley Police (TVP) arrested a 29-year-old woman and a 31-year-old man, both from London, after a report two trespassers had been in the grounds of the Royal Lodge at Windsor Great Park on the afternoon of April 25.
Police said there was no risk to any individual on the site.
Officers were also called to the Duke of York's home after a woman reportedly talked her way into his mansion on April 19.