The toll from the strike in the Wadi al-Kafur area of Nabatieh is one of the largest in southern Lebanon since Hezbollah and Israeli forces began exchanging near-daily fire over their border after war in the Gaza Strip began in October.
International mediators have been trying to reach a Gaza ceasefire between Israel and Hamas Palestinian militants, which diplomats say could help to avert a wider war in which Lebanon would be on the front line.
The death toll from the latest strike included "a woman and her two children" while five other people were wounded, most of them also Syrian, Lebanon's health ministry said in a statement.
The official Lebanese National News Agency reported that the casualties were Syrian refugees and workers.
Israel's military, on its Telegram channel, said the air force had struck a weapons storage facility of Lebanon's Hezbollah overnight "in the area of Nabatieh", which is about 12 kilometres (seven miles) from the nearest point of the Israeli border.
Following the deaths in Wadi al-Kafur, Hezbollah said it responded with a volley of Katyusha rockets on Ayelet HaShahar, a community in northern Israel.
None of the roughly 55 projectiles caused any reported injuries but they sparked "multiple fires", Israel's military said.
Earlier, around 20 kilometres to the north "a projectile that crossed from Lebanon" wounded two soldiers, one of them severely, in the Misgav Am area, Israel's military said.
The killings in quick succession in late July of Fuad Shukr, a top operations chief of Hezbollah in south Lebanon, and Hamas political chief Ismail Haniyeh, led to vows of vengeance from Hezbollah, Iran and other Tehran-backed groups in the region which blamed Israel.
Israel claimed the killing of Shukr, in a strike on south Beirut, but has not commented directly on the killing of Haniyeh while he visited Tehran.
In an effort to avert a broader conflict, Western and Arab diplomats have been shuttling around the region.
On Thursday, mediators made a new bid to push Israel and Hamas toward a ceasefire in Gaza. Talks took place in the Gulf emirate of Qatar and continued on Friday.
The negotiations are set to resume in Cairo "before the end of next week", the Egyptian, Qatari and United States mediators said in a joint statement.
In Beirut on Friday, Egyptian Foreign Minister Badr Abdelatty, after meeting his Lebanese counterpart Abdallah Bou Habib, expressed hope for "good intentions and the political will to reach this urgent deal" in Gaza.
The cross-border violence between Lebanon and Israel has killed 580 people in Lebanon, mostly Hezbollah fighters but including at least 128 civilians, according to an AFP tally.
On the Israeli side, including in the annexed Golan Heights, 22 soldiers and 26 civilians have been killed, according to army figures.
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