The shooting took place in the early hours after Israeli forces identified “suspicious movement” along the border.
It occurred near where a Lebanese army sniper killed an Israeli soldier late on Sunday. There was no information on the condition of the Lebanese soldiers.
The shootings raise the possibility of renewed fighting in the volatile area, which has remained mostly quiet since a month-long summer war in 2006.
The Lebanese army has opened fire in the past after saying Israeli soldiers had tried to infiltrate.
Lieutenant Colonel Peter Lerner, an Israeli army spokesman, said: “We will not tolerate aggression against the state of Israel, and maintain the right to exercise self-defence against perpetrators of attacks against Israel and its civilians.”
Since the 2006 war, the border has experienced only sporadic violence. Israel has responded with airstrikes and artillery fire following a number of rocket attacks and shootings across the border.
In the most serious incident, a high-ranking Israeli officer was killed by a Lebanese sniper in 2010 after Israeli forces tried to cut down a tree along the border. Israel responded with artillery fire, killing two Lebanese soldiers and a journalist.
Andrea Tenenti, a spokesman for UN forces in southern Lebanon, said the UN was informed of a “serious incident” along the border. He said the peacekeeping force Unifil was in contact with both the Lebanese and Israeli armies, and they were co-operating.
“The incident happened on the Israeli side of the blue line,” he said, referring to a UN-drawn line demarcating the border between the two enemy states. He gave no further details, saying Unifil was still investigating.