The National News Media and Hassan Abu Hamdan say the incident occurred early on Wednesday in the town of Hazarta.
Abu Hamdan says the family of the children, aged nine and three, was renting a substandard home in the town after fleeing the war in their homeland.
The incident underscored the perils facing the nearly 1.4 million Syrians who have escaped the fighting to seek refuge in neighboring Lebanon.
Many of the impoverished Syrians have crowded into shacks, tents and unfinished structures that offer meager shelter from the bitter cold, with no running water or electricity.
Syria's war has displaced nearly 9 million people, including 2.3 million refugees.
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