Sunday's death was the first in Israel from Hizb Allah fire since Israeli forces withdrew from south Lebanon three years ago and raised the prospect of Israeli retaliation against the group, its Syrian ally or Lebanon.
The sources said Hizb Allah fired anti-aircraft shells, which fell on the town of Shlomi, two days after the guerrilla group launched anti-tank rockets and mortar bombs at Israeli army posts on the border for the first time in seven months.
"An air defence unit of the Islamic resistance confronted ... Zionist enemy planes that violated Lebanese sovereignty over the western sector of south Lebanon," Hizb Allah said in a faxed statement.
Hizb Allah has been firing anti-aircraft shells sporadically in recent weeks in response to what it said were Israeli overflights of south Lebanon.
"Hizb Allah is playing with fire."
Israeli Deputy Defence Minister Zeev Boim
Some of the shells have hit Israeli communities, causing damage but no serious casualties.
"It's provocation by Hizb Allah ... they are not shooting anti-aircraft fire but fire against people. Hizb Allah is playing with fire," Israeli Deputy Defence Minister Zeev Boim told Army Radio after Sunday's incident.
"We have no desire to open a new front ... but we cannot agree to our people in the north being hurt."
Israel lodged a complaint with the United Nations after Friday's attack at Shebaa Farms, an area Hizb Allah regards as Lebanese territory and the United Nations has declared Israeli-occupied Syrian land.
Israeli ambassador Dan Gillerman warned Syria and Lebanon in a letter submitted to UN Secretary-General Kofi Annan that Israel would have "no option but to take the necessary measures to protect its citizens" unless they restrained Hizb Allah.
Hizb Allah said it launched Friday's attack in response to a car bombing, which the group blamed on Israel, that killed a Hizb Allah official in Beirut last week.