Bystanders said the blast rocked a car, killing at least one.
Hizb Allah's al Manar television said the bomb killed Ghalib Awali, 40, as he got into his car. It described him as "part of the leadership of the Islamic Resistance" - a reference to Hizb Allah.
Hizb Allah blamed Israel for the killing dismissing a Sunni group's claim as "enemy" attempts to stir discord.
"The assassination of one of the cadres of the Islamic Resistance has all the indications of being an operation carried out by the Zionist enemy," spokesman Shaikh Hasan Izz al-Din said.
"This is meant to stir internal discord and divisions among the Lebanese," he said.
"The Zionist enemy is behind this act that targets the resistance and one of its symbols, as well as the security and stability in Lebanon," he added
"This act was carried out by the Zionist enemy's security and intelligence services and networks, and the enemy should bear full responsibility for what it has done," he warned.
"This act was carried out by the Zionist enemy's security and intelligence services and networks..."
Shaikh Hasan Izz al-Din,
spokesman, Hizb Allah
The Hizb Allah statement was in response to an alleged underground Sunni Muslim group, the Jund al-Sham (Soldiers of Damascus), which claimed it was behind the killing.
Al-Manar showed pictures of the burned car and said it blew up when "one of the strugglers in the resistance" started the engine to leave his home.
A Lebanese security official said the blast went off just after 9am local time (0605 GMT) in the predominantly Shia Muslim neighbourhood of Harat Hraik, a Hizb Allah stronghold.
Hizb Allah said in a statement Awali died instantly, though a Lebanese security official said he was rushed to a nearby Hizb Allah-run hospital where he died soon after.
Hizb Allah played a leading role in helping end Israel's 22-year occupation of south Lebanon in 2000.
Israel assassinated the group's leader Abbas al-Musawi in 1992 in an air strike on his car.
Lebanon has tried and convicted several people in recent years of spying on and plotting against the group.