A bomber set off hidden explosives inside a public bus in in Al Tayaran square in the Bab-al-Sharji area at about 11.40am (0740 GMT) on Friday,
police Major Mohamed Younis said.
The blast occurred as the minibus was parked at a bustling bus station in the square.
There were conflicting accounts of the bomber's fate, however.
While Younis said the bomber detonated a belt of explosives strapped to his body beneath his clothes, eyewitnesses said they saw the man leave the bus minutes before it exploded.
Shopkeeper Nadhem Hassan said he saw a man "enter the bus and leave it very quickly", adding that he saw six burnt bodies in the vehicle.
"A man left a bag in a minibus shortly after he had boarded. It exploded just after he left," a police officer said. "Five people were killed and seven others wounded."
A US patrol came under a grenade attack in the al-Adhamiya district early on Friday, killing an Iraqi civilian, Iraqi journalist Walid Khalid told Aljazeera.
US soldiers are often attacked
while on patrol in Iraq
US forces suffered no casualties or material damage , he added.
Unidentified fighters also assassinated Ali Abd al-Rida Khalaf, an Iraqi Oil Ministry employee, in al-Shurta [police] tunnel west of Baghdad, he said.
Khalaf, killed in his civilian car, was also a member of the Iraqi al-Dawa party, led by the Iraqi Prime Minister, he added.
Fighters also assassinated former Iraqi army Brigadier Abbas Sultan Salam in front of his house in al-Sidiya neighbourhood in Baghdad, he said.
US soldiers killed
Meanwhile, a US soldier was killed and another wounded by a roadside bomb on a road linking the cities of Falluja and Ramadi, about 70km west of the Iraqi capital, the military said in a statement.
The explosion occurred while the soldiers were taking part in a combat logistics patrol on the road.
"A man left a bag in a minibus shortly after he had boarded. It exploded just after he left"
An Iraqi police officer
Also on Thursday, an Army soldier assigned to the 2nd US Marine Division was killed by small arms fire during an operation in Ramadi, the military said.
The names of the soldiers were withheld pending notification of their relatives.
The attack raised to at least 1912 the number of US military members who have died since the beginning of the Iraq war in March 2003.
Three officials in the Turkmen Front were killed and one wounded on Thursday by an unidentified armed group in Mosul, 390km north of Baghdad. An official in the group said they were attacked while leaving their office.
One policeman was also killed in the northern city on Thursday,, a police source said.
Six bodies of people who were shot dead were found on Thursday and Friday in different areas of Mosul, a medical source said.