The strike follows a bloody weekend rocket attack on the Israel-occupied Golan Heights, blamed by Israel on Hezbollah.
Israeli drone attacks have reportedly killed two people in southern Lebanon as conflict spirals between the bordering states.
The Israeli attack was the first lethal action following a rocket attack on Saturday that Israel says killed 12 children and youths in the Israeli-occupied Golan Heights. The strike has increased concern that the war in Gaza threatens to escalate into a regional conflict.
Lebanese state media said one strike hit a motorcycle close to the border, killing two riders and injuring a child. Two others were injured in a separate strike in southern Lebanon.
The Israeli military said it had struck Hezbollah operatives and infrastructure but did not give more information.
Israel has blamed Hezbollah for the rocket attack at the weekend. The pair has been pursuing a long campaign of low-level hostilities across the border for many months.
The Lebanese armed group, which is aligned with Iran and has pledged to continue to attack Israel in solidarity with Gaza, has denied responsibility.
Late on Sunday, Israel’s security cabinet authorised the government of Prime Minister Benjamin Netanyahu to retaliate.
Israel’s largest newspaper, Yedioth Ahronoth, quoted unnamed Israeli officials as saying Israel’s response would be “limited but significant”.
It listed options as ranging from a limited but “photogenic” attack on infrastructure such as bridges, power plants and ports, to strikes on Hezbollah weapons depots.
‘Chaos’ in Beirut
Anticipating Israeli counterattacks, Hezbollah and its affiliated groups evacuated some positions in parts of Lebanon and Syria that could be a target, the AFP news agency reported quoting a source close to the Lebanese group.
Fears of Israeli retaliation also extended to Beirut’s international airport.
The scene was chaotic on Monday morning at the Beirut international airport, as many airlines cancelled their flights and passengers queued up in cars outside the terminals, reported Al Jazeera’s Zeina Khodr.
“There is concern that the airport could be a target,” said Khodr from the airport. “Sources here told us that throughout the night, there were Israeli drones flying overhead.”
Both Israel and Hezbollah have appeared at pains to avoid a full-scale war since they began trading blows in October, mostly limiting their strikes to border zones and military targets.
But Khodr said “there is a lot of concern” in Lebanon that the latest wave of attacks could be a game-changer, leading to threats deeper in the country.
“The question is – will [Israel] hit Lebanon’s infrastructure [in response] or will they hit a Hezbollah target?” she said.
“The other question is – what will Hezbollah’s response be? If it is a measured response, then the conflict can be contained. But if it is not a measured response, then we are talking about this conflict, which has been largely confined to the border, widening.”
Randa Slim, a senior fellow at the Middle East Institute in Washington, DC, said Israel and Hezbollah are not interested in an all-out war anticipating mass displacement of their populations along conflict lines and because of how lengthy the fighting has become.
“I don’t think the Israeli prime minister is at this point interested in an all-out war, partly because there are uncontrollable, unpredictable consequences to a larger war in Lebanon, involving Hezbollah. Because eventually if it escalates, it will involve Iran as well,” said Slim.