Iraqi police on Wednesday named the woman as, Jamila Abbas Khumeidi saying that she was ''targeted because she was a high official of the Baath party''.
Khumeidi, is the former head of the Association of Iraqi women, which worked closely with the former government of Iraq.
In a separate incident in Kirkuk, a rocket slammed into the offices of a cultural centre. The attack on the al-Shafaq Kurdish cultural organisation is linked to the Kurdistan Democratic Party (DDP), according to members of the group.
The front of the building was damaged in the blast, but there were no reports of any injuries.
Ahmad Taqana, a member of the DDP said: ''I cannot accuse anyone but I believe there will be more attacks in the coming days.''
Meanwhile the governor of Najaf has called an open ended general strike in the province, to protest against the lack of security in the area.
The governor met members of the US-led occupation authority to discuss concerns about security following on from the killing of a judge.
A senior US official has admitted that continuing attacks in Iraq threaten American led efforts to rebuild the country after the war.
Deputy Defence Secretary, Paul Wolfowitz blamed the attacks on Baath party loyalists. He said the authority's priority is to involve more Iraqis in their country's defence.
Wolfowitz made his comments after the headquarters of the US-led occupation authority in Baghdad came under attack for the second time in as many days, injuring three people.