Family members added on Thursday that they had arranged a mourning ceremony to be held for him in the western city of Misurata.
"We learned of his death late Wednesday," one family member told The Anadolu Agency on condition of anonymity.
He said al-Zahawi had been seriously wounded while fighting in Benghazi, after which he was taken to hospital where he went into a coma.
He succumbed to his injuries on Tuesday, the family member said.
Ansar al-Sharia is deeply embroiled in the violence and struggles for wealth and influence that have engulfedLibya since a 2011 uprising toppled Muammar Gaddafi.
Its members have been battling the forces of former Libyan army general Khalifa Haftar since he declared war on the group in May, pushing it out of much of the Libya's second-largest city Benghazi.
The U.S. government blames Ansar al-Sharia for an assault on a former diplomatic compound in the eastern city in 2012, which killed the U.S. ambassador and three other Americans.
In the video recording announcing Zahawi's death, the militants swore revenge, according to SITE.
Al-Zahawi had fought against troops loyal to late Libyan leader Muammar Gaddafi in 2011.
In 2012, he founded the Ansar al-Sharia militia, which has a presence in a number of Libyan cities.
Libya has been suffering turmoil since Gaddafi's ouster and subsequent murder.