An investigation has been launched into the incident, a United Nations official said on Tuesday, declining to be identified.
The man's whereabouts when he was killed had earlier been disputed, with the Israelis saying he infiltrated their territory and Lebanese police saying they had found blood inside Lebanon.
The blood, according to the police, was near the barbed wire stretched along the Green Line drawn by the United Nations in May 2000 to delineate the frontier.
An Israeli military source said the soldiers shot the man after he entered Israel carrying sacks full of drugs.
According to the Israeli source, the man was seen near Maayan Baroukh kibbutz just after coming under the fence via a water-course. Soldiers first fired warning shots as the man tried to flee, the source said.
But Lebanese police said the Israelis had fired on two local shepherds, Jaafar and Ali Mustafa, as they tended their sheep near Wazzani village close to the frontier. Ali had returned home but Jaafar had vanished.