The strike late on Tuesday, part of a flare-up of border area hostilities between Israeli and Hezbollah forces, hit a home in the town of Bint Jbeil, where the powerful Iran-aligned Hezbollah enjoys widespread support.
The Lebanese-Australian civilian man was identified by one of his relatives as Ibrahim Bazzi.
His wife, a Lebanese citizen, also died.
Hezbollah then announced the killing of Ali Bazzi, his brother and one of the Shi'ite Muslim group's fighters.
Asked about the incident, the Israeli military said one of its jets had struck a Hezbollah military site overnight in Lebanon.
Hezbollah, an ally of Palestinian Islamist faction Hamas, has been exchanging near-daily fire with Israel across Lebanon's southern frontier sinc the eruption of the Israeli-Hamas war in Gaza in early October.
Hezbollah launched the most rockets and weaponised drones against Israel on Wednesday that it has in a single day since the spate of daily clashes began, security sources said.
The Israeli military said on Wednesday its jets had targeted a number of Hezbollah military sites and other locations.
Israeli air strikes and shelling have killed more than 100 Hezbollah fighters and nearly two dozen civilians, including children, elderly and several journalists.
