Police offered conflicting details on the bomber's identity, with one official saying a woman attacked the offices and another saying the bomber was believed to be a local supporter of Saddam Hussein's Baath Party who had left the area a few years ago and returned recently.
The two mangled bodies were found near each other, police said.
Ten of those killed were members of the anti-al-Qaida group, which has partnered with U.S. and Iraqi forces to rid their neighborhood of militants, said Brig. Gen. Mohammed al-Tamimi, the city police chief.
Another security official in the Muqdadiyah area said the bomber's head was found near the blast side and he was believed to be a local Baath supporter who recently returned to the area. The official identified the attacker as Suhail Hussein Ali, a man in his 40s.
A third police official said the head of a woman was also found and her body was badly disfigured, indicating she may have been wearing explosives. The two other officials spoke on condition of anonymity because they were not authorized to release details of the attack.
Violence is down nationwide in Iraq, but has increased in the north, where al-Qaida militants and other extremists are believed to have fled a U.S.-led security crackdown that began in mid-February in Baghdad .
The explosion went off about 9:30 a.m. on the outskirts of Muqdadiyah, about 90 kilometers (60 miles) north of Baghdad, on a road leading to the town market, al-Tamimi said.
As the influx of U.S. troops gained momentum earlier this year, American officials have courted both Sunni and Shiite tribal leaders around the country, hoping they will help lead local drives against al-Qaida and other militants. A similar effort saw some success in Iraq's westernmost province, Anbar, where Sunni tribes rose against the organization's brutality and austere version of Islam.
The groups now include some 60,000 Iraqis nationwide, most of them Sunni Arabs, according to the U.S. military, and members have come increasing attack from al-Qaida, which is trying to offset recent security gains.