The strikes in Habboush killed eight people, including a child and two women, and wounded 21 others, the ministry said, raising an earlier toll.
Other strikes in Zrariyeh killed four people, two of them women, and wounded four more, it said.
In Habboush, where the Israeli evacuation warning was issued, an AFP photographer saw clouds of smoke rising after the raids.
The state-run National News Agency (NNA) reported that Israeli warplanes “launched a series of heavy strikes … less than an hour after” the warning.
Israel’s military had said it would act “forcefully” against Hezbollah after the Iran-backed group’s “violations of the ceasefire agreement”, and told residents to flee to open areas at least one kilometre (0.6 miles) from the town.
The NNA also reported Israeli strikes and artillery fire on other south Lebanon locations, including the coastal city of Tyre.
Israel has kept up deadly strikes on Lebanon despite the April 17 ceasefire that sought to halt more than six weeks of war between Israel and Hezbollah.
The ceasefire text grants Israel the right to act against “planned, imminent or ongoing attacks”.
Israeli soldiers are operating inside a “Yellow Line” running some 10 kilometres (six miles) deep inside Lebanon’s border, where they are carrying out wide-scale detonations and demolitions of buildings.
The NNA said Israeli troops carried out detonations in the southern town of Shamaa, and “demolished a monastery and a school” run by a religious order in the town of Yaroun after other detonations of “homes, shops and roads” there.