The Israeli air force "struck and eliminated" Khodr Said Hashem, a naval unit commander for the Lebanese armed group, near the town of Qana, a military statement said.
It accused Hashem of "activities (that) posed a threat to the State of Israel and its citizens and constituted a blatant violation of the understandings between Israel and Lebanon".
The military said Hashem was a member of Hezbollah's elite Radwan Force and played a role in "maritime smuggling operations".
Lebanon's official National News Agency reported one person killed in an Israeli strike on a car in a village in the area of the southern city of Tyre, where Qana is located.
Hezbollah lawmaker Hassan Ezzedine called on a committee tasked with overseeing the November 27 truce deal with Israel to "put an end to this continued violation of our national sovereignty".
He also urged the committee to "exert all pressure to expel the enemy from the lands it occupies", warning that failure to do so would "push our people and our citizens to exercise their right to resist" them.
The truce deal largely halted more than a year of hostilities between Israel and Hezbollah, though Israel has continued to carry out strikes on Lebanese territory since the agreement took effect.
The fighting, initiated by Hezbollah in support of its Palestinian ally Hamas, included two months of all-out war and killed more than 4,000 people in Lebanon, according to authorities.
In Israel, 78 people were killed, as well as 56 troops killed inside Lebanon.
Hundreds of thousands have been displaced in Lebanon, according to the UN, and 60,000 in Israel.
Under the terms of the ceasefire, Israel was due to complete its withdrawal from Lebanon by February 18 after missing a January deadline, but it has kept troops at five locations it deems "strategic".
The ceasefire also required Hezbollah to pull back north of the Litani River, about 30 kilometres (20 miles) from the border, and to dismantle any remaining military infrastructure in the south.
Last week, Defence Minister Israel Katz said Israeli forces would remain indefinitely in what he called a "buffer zone" in south Lebanon.
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