Aqila al-Hashimi was declared clinically dead late on Wednesday night.
She had undergone two unsuccessful stomach operations at a US military hospital in the compound of Saddam Hussein's former Republican Palace in Baghdad.
US occupation administrator, Paul Bremer, released a statement offering his "condolences to her family, her colleagues on the Governing Council and the people of Iraq".
Council chairman and convicted fraudster Ahmad Chalabi, speaking from New York, said al-Hashimi was certain to be missed.
One of only three women on the 25-member US-installed council, she had been preparing to leave for this week's UN General Assembly meeting in New York.
But six men threw hand grenades and sprayed her two-car convoy with machine-gun fire on her way to the airport last Saturday.
Al-Hashimi is said to have been a
friend of Tariq Aziz, the former
deputy prime minister
Chalabi blamed Saddam Hussein loyalists for the shooting.
It was the first such attack on an Iraqi official of the US-appointed administration.
Members of Iraq’s governing council have all increased their security and have felt increasingly threatened since the weekend attack, according to Aljazeera’s correspondent.
“There is a popular perception is that the Governing Council is nothing more than a US government by proxy. Members now believe they are likely targets.”
Al-Hashimi, a career diplomat, had been expected to become Iraq's new ambassador to the UN.
She served in the Foreign Ministry during Saddam Hussein’s presidency and was the only official of the ousted government appointed to the 25-member Governing Council.