The bombing on Tuesday occurred in the town of Hilla, about 100km south of Baghdad, close to where another police chief was shot and killed a week ago and nine police recruits died when fighters sprayed their minibus with small arms fire.
Police Major Ali Jawad said guards outside the house of Hilla police chief Brigadier General Qais Hamza opened fire at the car when they saw it speeding toward them, but failed to stop the bomber.
Four of the wounded were guards and the three others residents of nearby houses, Jawad said. Hamza and his family, who were home at the time, were unhurt. The explosion damaged the chief's house and those of his neighbours.
Fighters regularly target the police because they view them as collaborators with the US-led occupation, and they often make easier targets because they are less well-armed and protected than the US occupation troops.
East of Baghdad in Diala province late on Monday, a US soldier from the 3rd Brigade of the 1st Infantry Division was wounded when a rocket-propelled grenade was fired at an army convoy, a US official said on condition of anonymity.
Also on Monday, west of Baghdad, a bomb explosion near a US military convoy killed an American soldier, a US official said. The attack occurred north-west of the town of Falluja.