Hizbollah said its fighters had downed the drone near the town of Aita Al Shaab.
Israel, which is technically at war with Lebanon, late last month said it had repelled an attempt by Hizbollah fighters to penetrate the border.
Hizbollah denied any involvement in the incident, which came after an alleged Israeli missile attack hit positions of Syrian government forces and their allies south of Damascus, killing five.
Hizbollah at the time said one of its own was among the dead and it vowed to respond.
Hizbollah had in September 2019 vowed to down Israeli drones overflying Lebanon following an incident a month earlier when two drones packed with explosives targeted Hizbollah's stronghold in south Beirut.
Lebanon and Israel are still technically at war, and the United Nations force, UNIFIL, patrols the border between the two.
Set up in 1978, UNIFIL was beefed up after a month-long devastating war in 2006 between Israel and Lebanon's Hizbollah.
The 10,500-strong force, in coordination with the Lebanese army, is tasked with monitoring a ceasefire and Israeli pullout from a demilitarised zone on the border.