The three children, two sisters and their cousin, were living in the hut built a year ago on the roof of a building in the northern Bhannine region.
"The parents had gone out to work and buy things and the children were alone," the official said, speaking on condition of anonymity.
"There was a gas leak and the flames devoured the hut," he added.
"The little bodies were charred and there was nothing of the place left."
More than 1.1 million Syrians have fled their country's conflict to take refugee in Lebanon, which has struggled to deal with the influx.
Many of the refugees live in dire conditions, in makeshift tents and huts and unfinished buildings.