A border escalation would be "very serious", says the UN
The raids were in apparent retaliation for attacks on Israeli army positions in the disputed Shebaa area.
Tension has been rising on the border recently, sparking concern that a second front could open up for Israel.
The raids came as Israel demanded that the United Nations take action to prevent new guerrilla attacks.
A foreign ministry spokesman warned that Israel was effectively putting Syria and Lebanon - which back Hezbollah - on notice that it would act against border provocations.
Israel withdrew from southern Lebanon nearly two years ago, after two decades of occupation.
The UN has endorsed Israel's withdrawal as complete. However Lebanon, Hezbollah and the Syrians claim the Shebaa area is Lebanese territory.
Katyusha incident
Lebanese officials said Israeli jets fired at least three rockets on targets south of Kfar Chouba village late on Tuesday after Hezbollah guerrillas fired mortar rounds and rockets at Israeli positions in the Shebaa area close to the Lebanese-Syrian border.
The clashes halted after about 80 minutes.
Hezbollah said one of its fighters had been killed "while carrying out his task in the framework of holy war".
Earlier on Tuesday there were also reports that a Hezbollah had fired a Katyusha rocket into northern Israel.
However Hezbollah, Lebanese security services and UN peacekeepers in southern Lebanon all said they knew nothing about the incident.
Hezbollah 'deploying on border'
At the UN in New York, the Israeli Government delivered a letter to Secretary General Kofi Annan, warning that recent attacks against Israeli civilian and military targets could have "alarming consequences on the stability of the region."
The letter from Foreign Minister Shimon Peres urged Mr Annan to intervene immediately and persuade the governments of Lebanon and Syria to take steps to prevent violations of Israel's northern border.
Israel says that in the past two weeks, armed groups have launched several attacks on Israeli military and civilian targets.
Mr Peres also said there is growing evidence that in recent days Hezbollah have started deploying armed men along the "blue line" monitored by the UN separating Israel and southern Lebanon.
A spokesman for Mr Annan said UN monitors are still trying to confirm the reported missile attacks from southern Lebanon.
He said the concern is that a second front of fighting might open up in what is already a very dangerous situation.