The Telal Sejoud area lies in Iqlim al-Touffah district, mountainous ridge around 20km north of the Israeli border where UN peacekeepers have a mandate to operate.
Lebanese military officials identified the dead officer as Samer Hanna, a first lieutenant, and said an investigation into the incident had been launched.
The area was considered a Hezbollah stronghold during the Israeli occupation of southern Lebanon and witnessed fierce battles before Israel's withdrawal in 2000.
As part of the ceasefire deal that ended the devastating 2006 war between Hezbollah and Israel, the army deployed in southern Lebanon along with a strengthened United Nations peacekeeping force.
Nine Lebanese soldiers and five civilians were killed in a bombing at a bus stop in the northern port city of Tripoli earlier this month in an attack thought to have been aimed at the army.