Set up in 1978, UNIFIL was beefed up after a month-long devastating war in 2006 between Israel and Hezbollah, Lebanon's Iran-backed Shiite militia
The Israeli army reported a "security" incident near the Lebanon border on Tuesday, and told local residents to seek shelter.
Lebanon had earlier rejected an Israeli call to reform a UN peacekeeping force patrolling the border ahead of a UN Security Council vote to renew its mandate.
Lebanon and Israel are still technically at war, and the United Nations force, UNIFIL, is tasked with monitoring a ceasefire.
The Israeli army said in a statement a "security incident" was "evolving" in the area of Manara, a kibbutz near the UN-demarcated Blue Line border in northern Israel.
"A number of routes in the area have been blocked. Any kind of activity in open areas is forbidden, including agricultural work," the army added.
"Residents are asked to remain in their houses, and near shelters, ready to find shelter upon immediate notice."
The army gave no information on the nature of the incident, which comes after Lebanon's Iran-backed Hezbollah movement announced at the weekend that it had brought down an Israeli drone flying over the Blue Line border.
Hezbollah vowed in September last year to down Israeli drones flying over Lebanon, following an incident a month earlier when two drones packed with explosives targeted the group's stronghold in south Beirut.
Set up in 1978, UNIFIL was beefed up after a month-long devastating war in 2006 between Israel and Hezbollah, Lebanon's Iran-backed Shiite militia.
The 10,500-strong force, in coordination with the Lebanese army, is tasked with monitoring a ceasefire and Israeli pull-out from a demilitarised zone on the border.
Israel accuses Hezbollah of stockpiling weapons at the border to prepare for a new war.