In a statement, the ministry said the deadly "Israeli enemy strike" had hit a vehicle in Burj Rahal.
Lebanon's state-run National News Agency said the attack took place near a school, causing "panic and terror" among the students.
The Israeli military said it had killed Hussein Jaber Dib, accusing him of belonging to Hezbollah's elite Radwan Force.
Israel has repeatedly bombed Lebanon despite a November 2024 ceasefire that sought to end more than a year of hostilities with Hezbollah, and has escalated its attacks in recent days.
The army said it had killed around 20 people "whose activities violated the understandings between Israel and Lebanon" over the past month.
Israel warned Sunday that it would intensify its attacks against the Iran-backed group, with Defence Minister Israel Katz claiming Hezbollah was "playing with fire, and the president of Lebanon is dragging his feet".
Hezbollah was badly weakened during the war, and the United States has pressured Lebanon to disarm it.
On Tuesday, Lebanese President Joseph Aoun reiterated his call for negotiations with Israel, saying the latter "has not yet defined its position and continues its attacks".
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