Monday's strikes came amid a new round of escalation between Israel and the militant Hezbollah group despite a truce reached more than two months ago.
Israel's military said late last week it has assumed "operational control" of the strategic Ali al-Taher hill that overlooks several villages and main roads leading to the city of Nabatiyeh.
The Health Ministry said one of the strikes hit a building, killing 11 people, including two children and four women. Eight were also wounded, including three children and a paramedic.
Another strike on a car in the village killed a paramedic with the Lebanese Islamic Risala Scout Association and wounded two others, the ministry said.
Israel said the strikes were in retaliation for two Hezbollah drone attacks from the area on Monday aimed at Israeli troops. It said they were targeting a militant trying to transport weapons to the village of Kafr Rumman.
Hezbollah did not claim the attacks nor immediately issue a statement on the intensifying strikes around Nabatiyeh province.
"We have been living in constant anxiety amid shelling on the outskirts," said Kafr Rumman resident Fouad Chakaron as he stood in front of the destroyed building. "Now they struck the heart of the town."
Another resident, Saleh Medlej, pointed to the destroyed building and said it had been home to families with children.
"Are there missiles here?" he asked in reference to the building where the families lived.
On Sunday, Israeli strikes killed at least seven people in southern Lebanon and levelled an empty hospital.
The strikes came days after Israel released five Lebanese prisoners as part of a deal between the two countries. In return, Lebanon agreed to search for the bodies of Jewish Lebanese citizens who went missing during the country's civil war decades ago.
A US-brokered truce in the region has repeatedly been violated, with Israel carrying out airstrikes in Lebanon and Hezbollah firing drones at Israeli troops.
Lebanon and Israel in June signed a framework deal under which Israeli forces were to withdraw from southern Lebanon in exchange for the disarmament of Hezbollah, but little progress has been made in its implementation.
Hezbollah is not a party to the Lebanon-Israel talks and has said it will not give up its weapons in any area north of southern Lebanon's Litani River.
Israeli officials, meanwhile, have said they will not withdraw unless Hezbollah is disarmed throughout the country.
Kafr Rumman's mayor, Abdullah Farhat, described what happened in the village as "a massacre in every sense of the word".
He blasted the framework agreement between Lebanon and Israel, saying Lebanese leaders "signed deals and we are paying the price here".
"There is an enemy that is not concerned about anything," Farhat said, referring to strikes that have been ongoing since the deal was signed.
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