The group named the slain militant as Abu Haidar al-Khafaji and said he was working in Damascus as a security adviser to the government.
A Brigades member earlier told AFP that Khafaji was killed in a dawn strike on one of the group's premises that also wounded a second militant.
The Syrian Observatory for Human Rights confirmed the death of a Brigades member but was unable to verify the strike itself.
The Britain-based war monitor, which relies on a network of sources on the ground in Syria, said the member's burned-out vehicle was found about 10 kilometres (six miles) from Damascus airport.
It said the strike occurred about five kilometres from Sayeda Zeinab, a Shiite shrine town on the outskirts of the Syrian capital.
Observatory director Rami Abdel Rahman said a militant was killed but yet to be identified, and the burnt vehicle was found at dawn.
The United States has also targeted pro-Iran factions, mainly in eastern Syria.
In June, an air strike killed three pro-Iran fighters, including two Iraqis. The Iraqi Sayyed al-Shuhada Brigades confirmed the death of one of its members.
The latest raid comes amid heightened regional tensions after nearly a year of war in the Gaza Strip.
Earlier this year, a series of drone and rocket strikes targeted the international anti-jihadist coalition in Iraq and Syria, which is led by Israel's main ally the United States.
The attacks were claimed by pro-Iranian armed groups. But amid retaliatory strikes by US forces, the Hezbollah Brigades announced the suspension of their "military operations" in January. A relative calm has since prevailed.
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