The strike, which Israel has not commented on, comes after 310,000 people, mostly Syrians, have in recent days fled to the neighbouring country, also the target of Israeli strikes.
Israel claims Hezbollah is using the Lebanon-Syria border crossing to transport weapons but it has provided no evidence for such claims.
It follows an intense night of bombardment of Beirut's southern suburbs, with a US and an Israeli news website saying Israel targeted Hezbollah's potential successor just a week after it killed its leader, Hassan Nasrallah.
The escalating assaults by Israel come as it weighs an attack against Hezbollah ally Iran for its retaliatory missile strikes.
President Joe Biden said on Thursday that the United States was "discussing" possible Israeli strikes on Iranian oil facilities.
Iran's supreme leader, Ayatollah Ali Khamenei, delivered a rare sermon on Friday, his first since his country's retaliatory missile attack on Israel, and also the first since Israel launched its wave of strikes on southern Beirut.
Thousands of Iranians were gathered in the capital Tehran with a photograph of Khamenei placed side by side with a picture of Nasrallah on the main stage.
Some carried the green and yellow flag of Hezbollah, while others carried the Palestinian flag.
In Lebanon, a source close to Hezbollah said Nasrallah had been given a temporary burial in a secret location until a public funeral could be held.
Buildings shook
Nearly a year since Israel's war on Gaza began, Israel announced it was shifting its focus to Lebanon.
Hezbollah started launching low-intensity strikes on Israel last October, in support of Palestinians suffering under Israel's assault on Gaza, forcing 60,000 Israelis to flee their homes in the north of the country.
Israel's bombing in Lebanon has killed more than 1,000 people since the start of the escalation on September 23, according to the Lebanese health ministry, and forced hundreds of thousands to flee their homes in a country already mired in economic crisis.
The overnight strikes on the southern suburbs of Beirut destroyed at least five buildings and left a huge crater in the road, an AFP photographer said.
A target of one of Israel's recent Beirut strikes was Hashem Safieddine, a potential successor to Hezbollah chief Nasrallah who was assassinated a week ago, US news site Axios said, citing three Israeli officials it did not identify.
Israeli news website Ynet also reported Safieddine had been the target, while the Israeli military told AFP it was looking into the reports.
On Thursday, the Israeli military claimed it had hit "targets belonging to Hezbollah's intelligence headquarters in Beirut".
Its Arabic-language spokesman Avichay Adraee accused Hezbollah of using the main international border crossing out of Lebanon into Syria to transport weapons.
Coastal Lebanon shares a border with Israel, with which Hezbollah is at war, and Syria.
Masnaa, as it is known, is the main overland crossing out of the country, and the strike could leave thousands who are unable to fly out trapped.
In Beirut, 35-year-old displaced nurse Fatima Salah said residents were "scared for our children, and this war is going to be long".
Israel announced this week that its troops had started ground raids into parts of southern Lebanon after days of heavy bombardment of areas across the country where the group holds sway.
Israel told Lebanese people Thursday to "immediately" evacuate more than 20 villages and the city of Nabatiyeh.
Hezbollah said it fought off Israeli troops on the border and set off two explosive devices against advancing soldiers.
The Lebanese group also said it kept up its rocket fire, with sirens warning of incoming fire blaring in northern Israel Friday.
Lebanon's health ministry said Friday that 37 people were killed and 151 wounded by Israeli strikes over the previous 24 hours.
The Israeli military said nine of its soldiers have been killed in combat in Lebanon.
The Iran link
Supreme leader Khamenei was delivering a sermon Friday, days after Iran launched its second-ever direct attack on its arch-foe Israel, in retalation for the killing of Nasrallah and other top figures.
Iranian Foreign Minister Abbas Araghchi meanwhile landed in Beirut for talks with Lebanese officials, Lebanon's official National News Agency reported.
Israeli Defence Minister Yoav Gallant warned that "those who attack the state of Israel, pay a heavy price".
Iran said it would step up its response if Israel counterattacked.
Israel claims to have intercepted most of the 200 missiles launched by Iran, though the attack has sparked fear in Israel of more violence to come. In the West Bank, a Palestinian was killed in an Israeli attack by shrapnel.
With fears of further violence drawing in more countries in the region, US President Biden said that "we can avoid" all-out war in the Middle East, but that "there is a lot to do yet, a lot to do yet."
Tulkarem strike
In the occupied West Bank, a source within the Palestinian security services told AFP that an Israeli air raid on the refugee camp of Tulkarem, which killed 18 people, was the deadliest in the territory since 2000.
The Israeli military said its strike in the northern West Bank killed Hamas leader Zahi Yaser Abd al-Razeq Oufi, who it accused of participating in numerous attacks.
Alaa Sroji, a social activist from the area, said an Israeli warplane "hit a cafeteria in a four-storey building".
Calls for restraint have multiplied but months of similar calls to halt Israel's war on Gaza failed to bring a ceasefire.
Israel's assault on Gaza has killed at least 41,788 people, mostly women and children, according to the territory's health ministry. The UN rights office has confirmed most of the dead are women and children.
*This story was edited by Ahram Online.
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