The blast on Thursday morning
scattered tangled metal and wreckage across Tahrir Square, a major intersection lined with shops and market stalls.
"We have received two dead and one wounded," said a paramedic at Kindi hospital.
A police officer at another hospital said four wounded had been admitted there after the blast.
US forces and Iraqi police sealed off the area, Iraqi journalist Ziyad al-Samarrai told Aljazeera. No US soldiers were injured.
Police said the target of the blast was not clear.
"A four-wheel drive car went off as US military vehicles passed but the convoy wasn't hit," Lieutenant Muhammad Salman of the Baghdad police said.
"It doesn't appear to be a suicide car," he added.
One witness, Ahmad Sabah Abid, said the driver of the car got out and ran away when the military convoy arrived at the square.
The blast occurred at around 8.30am (0530 GMT) and destroyed three cars.
A second car bomb killed wounded Iraqi police officers on patrol in the northern Baghdad suburb of Salman Pak, al-Samarrai reported on Thursday.
The bodies of more than 20 Iraqi drivers and security forces were found in their burnt-out convoy south of Baghdad on Thursday, AFP reported.
The bodies were found in a convoy of government trucks carrying sugar, which police said they thought was attacked at least two days ago and the bodies left to rot.
"This morning a police patrol was in the Suwairah region and
found about 20 vehicles that were taking sugar to Baghdad. They were all burned," said a police official.
Suwairah is about 60km south of Baghdad.
Two police officers and two soldiers who were protecting the convoy also were killed, the official said.
"The bodies were rotting in the vehicles, which indicates the
attack was at least two days ago," he said.
"Until now no one dared to remove the bodies, which are swollen and decomposing," he said.