Brigadier-General Abdul Karim Khalaf, an interior ministry spokesman, said the attack on Sunday took place at 11.20am (0720 GMT) near Baghdad's central Tayran Square.
The bomb detonated near a mobile phone shop near the square, a popular commercial area with shops specialising in electronic goods, photographers' equipment and mobile telephones.
Less than an hour later, a car bomb exploded behind a police station in the al-Alwiya district, killing a police officer and wounding five police commandos and two civilians, police official Mohammed Abbas Salman said.
Also on Sunday, Iraqi police found the remains of 14 more victims of a vicious sectarian conflict, some of them with severed heads.
Seven mutilated bodies were fished out of the Tigris river in the town of Suwayrah, at a spot southeast of the war-torn capital where murder victims wash up on a daily basis.
The bullet-riddled corpses of three men were found under a bridge on the road north from Baghdad to Balad.
Police also came upon three bodies during a raid on a warehouse in the capital, while another corpse was recovered in the southern city of Amara.
In Tikrit, the hometown of deposed Iraq leader Saddam Hussein, a petrol station manager was kidnapped by armed men, police said.
In the same province, an early morning clash between gunmen and the bodyguard of the provincial police chief left four fighters dead.
"Gunmen attempted to ambush the police chief's bodyguard who was with his companions and in the ensuing gunfight, the four were killed," a police officer said.
A roadside bombing in the east Baghdad neighbourhood of Jadida wounded two policemen.