The blast came at a time of prolonged political paralysis in Iraq caused by sectarian tensions. It followed a series of attacks that killed 17 people in Baghdad last week.
Adel Ahmed, an employee at the nearby Baghdad Health Department, said he was reading a newspaper in his office when he heard the blast at around 11 a.m.
"The ceiling fell on my head and I was slightly wounded in the head and fell down," Ahmed told The Associated Press by phone. He said walked to the scene of the explosion and saw wounded people on the ground screaming for help. "The scene was horrific," he said.
Two police officials said the explosives-rigged car was parked in a parking lot near the religious affairs building and the health department. The front of the three-story religious affairs office collapsed from the impact of the blast. Firefighters were searching the debris for survivors. The blast also shattered nearby windows and damaged cars in the area.
The damaged building housed the so-called Shiite endowment, or department that supervises Shiite religious affairs, including holy sites and mosques across Iraq.
A doctor in a nearby hospital confirmed the casualty figures. All officials spoke on condition of anonymity as they were not authorized to release information.
Violence has fallen in Iraq since a wave of sectarian bloodshed in 2006 and 2007, but insurgents carry out frequent attacks on security forces and civilians to undermine the Shiite-led government following the pullout of U.S. forces in December.
A unity government headed by Prime Minister Nouri al-Maliki, a Shiite, has been largely paralyzed since the withdrawal of the U.S. troops.
There is mounting criticism of al-Maliki within the ruling coalition, over complaints that he is shutting out Iraq's two main minorities -- Kurds and Sunni Muslims -- in decision-making. However, his opponents appear to fall short of a needed majority in parliament to bring down him down.