It says Tariq bin al-Tahar bin al-Falih al-Awni al-Harzi was responsible for co-ordinating suicide bombings in Iraq and moving weapons from Libya to Syria.
IS has not commented on the reports of his death.
Harzi was allegedly killed in the northern-eastern Syrian town of Shaddadi on 16 June.
The US Treasury Department had placed him on a sanctions list after designating Harzi as a “global terrorist”.
It is thought that he had assisted foreign fighters from the UK, Albania, and Denmark.
He also raised funds for the group, including $2m from a single Qatar-based donor.
A Pentagon spokesman said Harzi’s death was a blow to Islamic State.
“His death will impact [IS’s] ability to integrate foreign terrorist fighters into the Syrian and Iraqi fight as well as to move people and equipment across the border between Syria and Iraq,” Capt Jeff Davis said in a statement.
In June the Pentagon said it had killed Harzi’s brother in a drone strike.