The Israeli army said it shelled Lebanon early on Tuesday in response to earlier rocket attacks, as the UN urged both sides to show "maximum restraint".
"Two rockets were fired from Lebanon into Israeli territory," the army said. It said one was intercepted by air defences and the other hit open ground.
"In response ... artillery struck in Lebanese territory," the Israeli army said.
The rockets were fired at Israel from the Qlaileh area of southern Lebanon, where a third rocket was also found, a Lebanese security source told AFP.
The source said the Lebanese army had not identified the group responsible for the launch.
The head of Israel's army, Aviv Kohavi, speaking at a northern military base, said the country would "respond either openly or in secret, or both at the same time, to every violation of our sovereignty".
The UN peacekeeping force in the border region said it had boosted security in the area and "launched an investigation" in collaboration with Lebanon's military.
It said it was "in direct contact with the parties to urge maximum restraint and avoid further escalation".
The last time rockets were fired from Lebanon into Israel was in May, during an 11-day conflict between Israel and Palestinian armed groups in the Gaza Strip.
In recent weeks, Israeli officials have expressed growing concern over the deepening economic crisis in Lebanon and its ramifications for border security.
"The state of Lebanon is responsible for the rockets fired overnight, as it allows terrorists to operate within its territory," Defence Minister Benny Gantz tweeted.
"We will not allow the social, political and economic crisis in Lebanon to turn into a security threat to Israel.
"I call on the international community to take action to restore stability in Lebanon."