A position of the Popular Front for the Liberation of Palestine-General Command near Qusaya was hit, the state-run National News Agency reported.
The group responded with a barrage of anti-aircraft fire, it added.
On Sunday, the Iran-backed Hezbollah movement accused Israel of trying to carry out a drone attack in Beirut.
After two drones came down in the capital, Hezbollah leader Hassan Nasrallah said its fighters would shoot down any drones that entered Lebanese airspace.
Two Hezbollah members were killed on Saturday night when Israel struck targets in Syria to prevent what it said was a drone attack by Iranian forces and their allies.
The National News Agency reported that Israel carried out three air strikes on the outskirts of Qusaya, a village in the Bekaa valley near the border with Syria, early on Monday.
A top official from the PFLP-GC told the BBC that a drone carried out the raid.
There were no reports of any casualties and the Israeli military did not comment.
The PFLP-GC has been operating in Lebanon for decades and has close ties to the Syrian government, whose forces it has supported in the country’s eight-year civil war along with Hezbollah.
“This aggression is a continuation of what happened in Beirut and a provocative attempt that is a direct reaction to Nasrallah’s statements,” Khaled Jibril, a PFLP-GC official, told al-Mayadeen TV.
Early on Sunday, two drones that the Lebanese army said were Israeli crashed in the southern Beirut district of Dahia, which is dominated by Hezbollah.
One of the drones hit a building that houses Hezbollah’s media office, while the other exploded and crashed nearby, causing material damage.
Again, no-one was injured and Israel declined to comment.
“What happened… was an attack with a suicide drone,” Hassan Nasrallah said in a televised speech later on Sunday. “This is the accurate description.”
The Hezbollah leader called it a “very, very, very dangerous development” and a “clear breach of the rules of engagement” established after the month-long war between Hezbollah and Israel in 2006.
“The time when Israeli aircraft come and bombard parts of Lebanon is over,” he warned. “I say to the Israeli army along the border: from tonight be ready and wait for us.”
Lebanese President Michel Aoun, a Hezbollah ally, said on Monday: “What happened was similar to a declaration of war which allows us to resort to our right to defending our sovereignty.”
“We are a people seeking peace not war, and we don’t accept anyone threatening us in any war.
Prime Minister Saad Hariri, an opponent of Hezbollah, said Israel’s actions constituted “a threat to regional stability”.
Hassan Nasrallah also said the Israeli air strikes south-west of the Syrian capital, Damascus, on Saturday had hit a Hezbollah rest house and not a military facility.
An Israeli military spokesman said the strikes had thwarted a plan by the Quds Force, the overseas operations arm of Iran’s Islamic Revolution Guard Corps (IRGC) and allied Shia militias to launch a number of attack drones loaded with explosives at targets in northern Israel.
IDF intelligence can now release the surveillance footage of Iranian Quds Force operatives in Syria carrying a killer drone that they intended to use for an attack on Israel.
How do you foil an attack of killer drones?
Killer intel. pic.twitter.com/5bgMvW61nr
— Israel Defense Forces (@IDF) August 25, 2019
A senior IRGC commander also denied that Iranian positions were hit.
Israel has been so concerned by what it calls Iran’s “military entrenchment” in Syria and shipments of Iranian weapons to Hezbollah that it has conducted hundreds of air strikes in an attempt to thwart them since 2011.
Meanwhile in Iraq, the powerful Iranian-backed paramilitary Popular Mobilisation force again accused Israel of what it said was a drone attack near the Syrian border in Anbar province on Sunday that killed two of its members.