Mustafa Amine Badreddine, 55, died in a large explosion near Damascus airport, the Lebanon-based militant group said in a statement on its al-Manar website.
He is charged with leading the assassination of former Lebanese Prime Minister Rafik Hariri in Beirut in 2005.
Hezbollah supports Syria’s President Bashar al-Assad and has sent thousands of fighters into Syria.
The US treasury, which imposed sanctions on Mustafa Amine Badreddine last July, said at the time he was “responsible for Hezbollah’s military operations in Syria since 2011, including the movement of Hezbollah fighters from Lebanon to Syria, in support of the Syrian regime”.
Lebanon’s al-Mayadeen TV had earlier said that Mustafa Amine Badreddine died in an Israeli airstrike. Israel has not commented on the claim.
Announcing Mustafa Amine Badreddine’s death, Hezbollah said in an initial statement: “He took part in most of the operations of the Islamic Resistance since 1982,” referring to the group’s military wing.
The second statement, on al-Manar’s website, said: “The investigation will work on determining the nature of the explosion and its causes and whether it was a result of an air, missile or artillery attack.
“We will announce further results of the investigations soon.”
Al-Manar said Mustafa Amine Badreddine would be buried in Beirut on May 13.
Born in 1961, Mustafa Amine Badreddine is believed to have been a senior figure in Hezbollah’s military wing.
He was a cousin and brother-in-law of Imad Mughniyeh, who was the military wing’s chief until his assassination by car bomb in Damascus in 2008.
According to one report, a Hezbollah member interrogated by the Canadian Security Intelligence Service (CSIS), described Mustafa Amine Badreddine as “more dangerous” than Imad Mughniyeh, who was “his teacher in terrorism”.
Mustafa Amine Badreddine and Imad Mughniyeh are alleged to have worked together on the October 1983 bombing of the US Marine Corps barracks in Beirut that killed 241 personnel.
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