The blaze took hold at the camp near Qab Elias town in the Bekaa Valley. Footage from the scene showed near total devastation.
The UN refugee agency told Reuters the camp had housed 102 families.
Lebanon has one million registered Syrian refugees, but believes the number is more like 1.5 million.
Many Syrians, displaced by more than six years of fighting in their own country, live in makeshift camps dotted around Lebanon.
The UNHCR's Dana Sleiman said it is thought the fire was caused by a cooking stove, but added "we are waiting to confirm it".