"A surveillance drone of the Israeli enemy" overflew "the area of Bint Jbeil at medium altitude" in the morning, the statement said.
"Army anti-aircraft batteries opened fire on the drone, forcing it to gain altitude before leaving Lebanese airspace."
The country's military reports almost daily on airspace violations by Israeli aircraft, but does not normally open fire at them.
"To the best of my knowledge, there's probably no other country in the world -- probably, I may be wrong -- which is subject to such an intrusive regime of aerial surveillance," UN special envoy for Lebanon Michael Williams said this month.
Resolution 1701 brought an end to the 2006 war between Israel and Hezbollah militants based in southern Lebanon, although the accord has failed to seal a permanent ceasefire.
It mainly insists on the strict embargo on providing arms to Lebanese militias, while also affirming the Beirut government's sovereignty across the whole country.