"Mahmud al-Arfan, who was 18 months old, was burned alive when the tent where his family lived caught fire," the official told AFP on condition of anonymity, adding his death had been confirmed.
The child was alone in the tent when a diesel-powered heater caught fire in a makeshift refugee camp on the road between the southern Lebanon towns of Ras al-Ain and Naqura.
His parents were out working in the fields at the time.
Two young men who rushed to put out the flames suffered from burns and smoke inhalations.
More From This Section
The toddler's parents are originally from Aleppo, in northern Syria, but have spent the past nine months in southern Lebanon.
The baby's father has two wives and 12 other children.
The United Nations have moved the family to the nearby village of Kneisseh, where they will be given a new shelter.
"Most of the men and women were in the fields, where they work as day labourers. We saw flames, and we ran to the place where the fire had broken out, to try and extinguish it," said Ali Jumaa Mansour, a supervisor at the makeshift camp.
According to the United Nations High Commissioner for Refugees, more than 842,000 Syrians have fled to Lebanon since Syria's conflict broke out in March 2011.
Lebanon is hosting the highest number of Syrian refugees in the region, followed by Turkey and Jordan.
While both Turkey and Jordan have opened official refugee camps at the borders with Syria, Lebanon's government has refused to do so.
Thousands of refugees now live in apartments -- either as relatives' guests or as renters.
But thousands of others, who cannot afford the cost of living in Lebanon's cities, shelter in hundreds of informal tent settlements scattered across the country.