The Israeli military said the commander was killed when Israel struck the southern suburbs of Beirut.
There was no immediate confirmation from Hezbollah.
Prime Minister Benjamin Netanyahu and Defence Minister Israel Katz announced the attack in a joint statement on Wednesday.
The strike has raised pressure on the ceasefire that had halted Israeli attacks on Beirut, even as Israeli forces have remained deployed in areas south of the Litani River and continued to carry out strikes in southern Lebanon.
Iran ally Hezbollah has responded to those strikes by firing and launching armed drones towards Israeli soldiers.
The Lebanon ceasefire has underpinned a broader truce in the wider Iran war, with a halt to Israeli strikes in Lebanon being a key Iranian demand in Tehran's negotiations with Washington.
Israel earlier on Wednesday called for residents to evacuate several villages north of the Litani River, which could represent an expansion of Israel's zone of action.
Talks between Israel and Lebanon have continued, but have largely been at the ambassador level.
Lebanese Prime Minister Nawaf Salam said on Wednesday that it was premature to talk of any high-level meeting between Lebanon and Israel.
Salam, in comments reported by Lebanon's National News Agency on Wednesday, said shoring up a ceasefire would be the basis for any new negotiations between Lebanese and Israeli government envoys in Washington.
Washington in April hosted two meetings between the Israeli and Lebanese ambassadors to the United States.
Hezbollah strongly objects to the contacts.
Since Hezbollah triggered the war by opening fire in support of Iran on March 2, the Lebanese administration led by Salam and President Joseph Aoun has initiated Beirut's highest-level contacts with Israel in decades, reflecting deep divisions between the Shi'ite Muslim group and its Lebanese opponents.
Announcing a three-week extension of the Lebanon-Israel ceasefire on April 23, US President Donald Trump said he looked forward to hosting Netanyahu and Aoun in the near future, and that he saw "a great chance" the countries would reach a peace deal in 2026.
Israel has carved out a self-declared security zone extending as deep as 10km into southern Lebanon, saying it aims to protect northern Israel from Hezbollah militants embedded in civilian areas.
Lebanon's health ministry said on Wednesday an Israeli air strike killed four people including two women and an elderly man in the town of Zelaya in southern Lebanon.
The Israeli military said Hezbollah had launched explosive drones and rockets towards Israeli soldiers in southern Lebanon, injuring two Israeli soldiers.
