Al-Khufayi's son, Ahmad, however, did not survive the attack and reports indicated he drowned on Thursday after his car crashed in a river.
"The head of Khufaji's protection unit told our correspondent in Baghdad that her son, Ahmad, drowned when the car in which he was travelling fell in a river," Aljazeera television reported
A bodyguard was also killed.
Salam al-Khufaji herself had not been hurt in the attack.
An Iraqi official in Baghdad told AFP she escaped unharmed when her convoy came under attack at Yusufiyah, 20 kilometres south of the Iraqi capital, as she returned from a trip to Najaf.
According to medical sources at Al-Yarmuk hospital in Baghdad, two bodyguards were also injured in the incident.
Al-Din Salim was killed in car
bombing attack on 17 May
Al-Khufaji, a dentist, replaced another woman on the council who was killed in an attack outside her Baghdad home in September last year. Akila al-Hashemi, a secular Shia Muslim, died three days after being shot.
The interim council's rotating chairman Izz al-Din Salim was killed ten days ago in a bombing outside the headquarters of the US-led occupying forces in Baghdad.
In other developments, a leading Sunni Muslim scholar was killed and one of his colleagues wounded by unknown attackers in Iraq, according to a statement from the Association of Muslim Scholars.
"The committee is furious after Saadi Ahmad Zaidan was assassinated and Khalid Soulaiman al-Fahdawi seriously wounded," it said without giving any details of when or where the attack took place.
"The committee is furious after Saadi Ahmad Zaidan was assassinated and Khalid Soulaiman al-Fahdawi seriously wounded"
Statement from Association of Muslim Scholars
The attackers' motive was to "sow sedition between Muslims at a time when the country aspires to unity ... to overcome the stalemate of occupation," it added, referring to the US-led occupying forces in Iraq.
The group of top Sunni scholars called its supporters to show self-restraint and obey Islamic law.
Another member of the committee, Shaikh Ahmad Abd al-Karim al-Ani, sustained multiple bullet wounds after being shot outside a Baghdad mosque on Sunday.
Early on Friday morning, Japan's foreign ministry said it was checking information that two Japanese nationals had been
attacked near Baghdad.
"The Japanese embassy in Iraq received the information Thursday that a motor vehicle carrying two Japanese people had been attacked, and we are trying to confirm it urgently," a ministry official said.
The public network Japan Broadcasting Corp said two Japanese men, possibly journalists, had been attacked some 30 kilometres (20 miles) south of Baghdad.
Their car caught fire but their fate is unknown, the network
said, adding the information was given to the Japanese embassy by an Iraqi driver.