The raid on Saturday represent a major escalation by Israel.
Lebanese Prime Minister Nawaf Salam said his country was at risk of being drawn into a “new war” as dozens of other Israeli air strikes killed at least five people.
Salam warned Israel’s “renewed military operations on the southern border” would bring “woes to Lebanon and the Lebanese people”.
Israeli artillery and air strikes hit southern Lebanon after its military said it intercepted three rockets launched from a Lebanese district about 6km (4 miles) north of their shared border. Israel said it targeted rocket launchers it claimed belong to Hezbollah, which it holds responsible for the launches.
The Lebanese group issued a statement denying any involvement in the series of rocket attacks on northern Israel from southern Lebanon.
In its statement, Hezbollah accused Israel of creating a pretext to renew its air attacks and reiterated its commitment to a ceasefire signed in November, which ended a year of war between the two sides.
Defence Minister Michel Menassa has stated the Lebanese army has begun investigating the circumstances of the rocket fire. He also called on the states sponsoring the ceasefire to “deter the Israeli enemy from its continued violations and attacks under flimsy pretexts and false pretexts”.
Saturday’s reported exchange was the first since Israel on Tuesday abandoned a separate ceasefire in the Gaza Strip with the Palestinian group Hamas.
Lebanon has blamed Israel for the protracted conflict after failing to withdraw from all Lebanese territory as stipulated in the ceasefire.
Under the deal, a January deadline was set for an Israeli withdrawal but Israel extended it to February 18. Since then, Israeli soldiers have remained in five locations inside Lebanon and its military has carried out dozens of deadly strikes against supposed Hezbollah targets, often striking civilians.
On Saturday, Salam declared that “all security and military measures must be taken to show that Lebanon decides on matters of war and peace”.
In a separate statement, Lebanese President Joseph Aoun condemned “attempts” to destabilise his country and reignite violence as he called for action to prevent a further escalation of the conflict.
Tel Aviv announced the attacks were “in response to the rocket fire at Israel”.