Police said Brigadier-General Numan Salman Faris, director of al-Azamiya district rapid response force, was shot by armed men in eastern Baghdad on Monday.
No further details were given.
Armed groups frequently target senior officers of Iraq's
security forces, whom they regard as collaborators with US-led forces.
Also on Monday, two rockets landed in the Oil Ministry complex in Baghdad, wounding an employee and damaging several vehicles.
Police said the missiles hit the main parking lot next to the ministry building.
Police Captain Nabil Abd al-Karim said only one exploded while the other failed to detonate.
The massive Oil Ministry was one of the few government buildings left undamaged in the air strikes and looting that accompanied the 2003 US-led invasion of Iraq.
In the past two years, however, the heavily fortified complex has been repeatedly targeted.
"Japan has received an official request to extend its presence in Iraq"
Japanese prime minister
Also on Monday, Japanese Prime Minister Junichiro Koizumi said Baghdad had asked Tokyo to extend its non combat mission of troops in the southern part of the country beyond its expiration in December.
Koizumi, in a debate with the leaders of five other major political parties in Japan, said that the government had not yet made a decision about whether it would extend the mission, which is opposed by many in Japan.
"Japan has received an official request to extend its presence in Iraq," Koizumi said.
"So we will continue to monitor the situation there, and make a comprehensive decision on the issue based on realities within the country, the opinions of the Iraqi people, US-Japan relations, and Japan's responsibilities in the international community," the prime minister said.
Japan has about 550 troops in the southern city of Samawa on a humanitarian mission to purify water, rebuild schools and other tasks.