"An initial enquiry confirmed that the sniper is a member of the Lebanese armed forces."
Mr Cohen, 31, was hit by a round of up to 10 shots.
An Israeli army spokesman, lieutenant colonel Peter Lerner, 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."
The Lebanese army is now on high alert in the area.
Mr Lerner protested to the United Nations border peacekeeping force Unifil over what he called an “outrageous breach of Israel's sovereignty".
Andrea Tenenti, a Unifil spokesman, said the shooting happened "on the Israeli side of the Blue Line", referring to the the border between the two countries, as recognised by the UN.
In 2006, Israel and the Lebanese militant group Hizbollah fought a month-long war.
