Hamas confirmed Mohammad Shaheen’s death but described him as a military commander.
The truce, now in its fourth day, is supposed to bring calm to war-battered Gaza for at least six weeks.
Gaza’s Health Ministry says more than 46,000 Palestinians have been killed in the Israel-Hamas war, with no end in sight to the 15-month conflict.
Thousands of people made their way into southern Lebanon, defying a warning from the Israeli military to stay away from previously evacuated areas.
The region braced for further escalation as Israel vowed to retaliate for Iran's ballistic missile attack a day earlier.
Israel and the United States have warned there would be severe consequences if Iran attacks.
Israel advised people to evacuate to the north of the Awali River, about 36 miles from the border and much farther than the Litani River.
It follows recent strikes in Lebanon and the assassination of Hezbollah leader Hassan Nasrallah, a significant escalation in the war in the Middle East.
Israel has dramatically escalated strikes, saying it is targeting Hezbollah’s military capacities and senior Hezbollah commanders.
The chief of Israel's army said Wednesday that the military is preparing for a possible ground operation in Lebanon.