A second Israeli soldier was injured in the incident on Monday, reported Israeli military officials.
Al-Manar television reported that Hizb Allah had destroyed the vehicle that crossed the border near the Lebanese town of Marwahine.
A statement released by Hizb Allah said: "It is not the first time that the enemy has been behind such violations in more than one border area."
The Israeli army commander on the Lebanon border, Maj. Gen. Benny Gantz, claimed that a bulldozer was clearing land on the Israeli side of the border when it was hit. He said it was hit with an anti-tank missile.
Earlier on Monday the United Nations condemned Israel for its persistent intrusions into Lebanese airspace since it ended its 22-year occupation of south Lebanon in May 2000.
Israeli jets violated Lebanon's airspace before today's incident, breaking the sound barrier and causing sonic booms.
"The United Nations expresses its dismay regarding the large number of Israeli air violations of the Blue Line (UN border demarcation) on 19 January, 2004, when 10 overflights were recorded," said UN representative Staffan de Mistura.
"Today's numerous overflights and anti-aircraft fire have disrupted some apparent restraint over the past two weeks in which no Israeli air violations were recorded and a longer period with no Hizb Allah anti-aircraft fire," he said.
Hizb Allah spearheaded efforts to oust Israeli occupation forces from south Lebanon.