An explosive device detonated at about 5:00am (02:00 GMT) on Friday, destroying an information office of the Supreme Council for Islamic Revolution in Iraq (SCIRI), Aljazeera's correspondent reported.
The dead woman is believed to be the aunt of a security guard, whose family live in the building.
Witnesses told the correspondent an aeroplane had flown overhead minutes before but it is not yet clear what caused the blast.
The apparent attack is the second such incident in a week. A senior official SCIRI, which has so far urged its followers not to take up arms against US-led occupation forces, was killed in the Iraqi capital on Wednesday by suspected pro-Saddam Hussein resistance fighters.
Led by Abd al-Aziz al-Hakim, SCIRI was founded in 1982 in opposition to Saddam's rule. Though still based in Iran, it is represented on the US-installed Governing Council.
Its previous leader, Muhammad Baqr al-Hakim, was killed by a car bomb in the Iraqi city of Najaf in August.