In a statement posted on a website commonly used by anti-government fighters, the Islamic State of Iraq, an al-Qaeda-linked group, said it was behind the attack .
The bomber blew himself up as al-Zubayi, one of two deputies to Nuri al-Maliki, the Iraqi prime minister, and other worshippers were leaving a mosque in the courtyard of his house, according to police.
Five of al-Zubayi's bodyguards were killed in the blast while Mufeed Abdul-Zahra, an adviser, was wounded in the attack and died later at the hospital.
The attack came a day after a rocket landed in the Green Zone as Ban Ki-moon, the UN secretary-general, and al-Maliki were holding a joint press conference.
Mahmud Othman, a Kurdish member of parliament, said Zubayi was al-Maliki's deputy on a ministerial committee for security, which was enough to make him "an important target".
But Imad Shahib, an Iraqi journalist, told Al Jazeera al-Zubayi was probably targeted simply "because he's part of the government and everyone here in Iraq is targeted".
Like other Sunni Arab politicians who agreed to join the Shia-led Iraqi government, al-Zubayi is routinely denounced by Sunni fighters as a traitor who betrayed his community in exchange for a cabinet post.
An alleged al-Qaeda umbrella group in Iraq supposedly cited by name al-Zubayi, along with Tariq al-Hashemi, the vice president, as "helpers" to the "crusader occupiers and their stooges".
Incidentally, al-Hashemi, who is currently visiting Japan, said on Friday that Iraq is living a "tragedy" and that the Iraqi government could not move beyond the situation without international assistance.
In other news, a US marine was killed in combat in Anbar on Thursday, the US military said. Also, a US soldier was killed by a roadside bomb that hit his patrol in western Baghdad, the US military said in a statement. It did not say when the incident happened.
On Wednesday, a US soldier was killed in Balad during combat, the US military reported on Friday.