The Shia Muslim fighters fired about 15 shells and rockets at Israeli positions in the area, and Israeli forces returned fire with artillery at the suspected source of fire near the Lebanese village of Kfar Chouba, witnesses said.
The Israelis fired about 45 shells, the witnesses said.
An Israeli warplane fired a missile at a position north of the village, Lebanese security officials and witnesses said.
An Israeli military spokesman said there were no casualties from the Hizb Allah fire. There was no immediate word on casualties on the Lebanese side from the Israeli retaliation.
An Israeli spokesman said Hizb Allah fired at least nine shells at army positions in the north and that the military responded with artillery.
The group's Al-Manar television said the attack was in retaliation for Israeli attacks on Lebanese territory, including a hit on civilian houses in the village of Kfar Chouba.
It said the fighters used "appropriate" weapons and scored a direct hit on the Ruaissat al-Alam position.
The clashes began after Israel
fired into Lebanon
"The Islamic Resistance warns the Zionist enemy that any attack on civilians will be met with the appropriate response," the statement said.
The heavy exchange came after days of sporadic shelling by both sides, which began when Israel mistakenly fired an artillery shell into Lebanon earlier this week while clearing explosives planted by the group near the border.
The Israeli army said the shell fell in an open area, causing no damage or casualties.
The increase in tensions comes amid political turbulence in Lebanon. Hizb Allah's ally Syria withdrew its troops from Lebanon last month, weakening Damascus's hold in the country, while Hizb Allah has been seeking a greater political role.
The group's years-long confrontation with Israel has been a major source of its popularity in Lebanon, even outside the country's Shia community.
About 2000 protesters at a Hizb Allah-orchestrated demonstration near the US Embassy in a northern Beirut suburb burst into cheers when news of the attack was announced.
Shebaa Farms are the scene of
periodic Hizb Allah-Israel clashes
The protest has become a weekly occurrence to demand Washington stop interfering in Lebanese affairs.
Hizb Allah sporadically attack Israeli forces in Shebaa Farms on the foothills of Mount Hermon where the borders of Syria, Lebanon and Israel meet.
A UN-drawn border that followed Israel's troop withdrawal from south Lebanon in 2000 left the area under Israeli control, but Lebanon claims it. The UN says the region is part of Syria and occupied by Israel.