The video, which was posted on YouTube yesterday and shared widely, shows the three terrified children crying as a man standing behind a camera waves a knife and asks: "Whom do we behead first?"
Adding to the pathos of the incident, the crying children respond by pointing at each other.
A security official said the video proved to be a "sick joke," and that the children had been left in the man's care by their mother, his neighbour, while she went to buy groceries.
While describing the incident as "an isolated incident," the official said the video was yet another sign of the effect of the Syrian war on Lebanese society.
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Lebanon hosts more than 1.1 million Syrian refugees, and fighting related to the conflict frequently breaks out in the tiny country.
Last month, jihadists took a number of Lebanese soldiers and police hostage after battles with them. They subsequently beheaded two of the soldiers, and widely distributed images of their corpses.
"People are affected by seeing images of beheadings, and some people will start to imitate them. Poor children; they were terrified," he added.