They said five mortars landed on the premises in Dujail, one of many around the country providing information to potential voters before the 30 January election. It will be used as a polling station on the day of the vote in six weeks.
Among the wounded were six Iraqi national guards, who were guarding the office against attack in the Sunni Muslim town, 50km north of the capital.
US and Iraqi officials have warned that fighters, who are determined to expel foreign forces from Iraq, could step up attacks before what officials hope will be Iraq's first free election in decades.
An influential Muslim group, the Association of Muslim Clerics, has called on Iraqis to boycott the poll in protest against US offensives on Falluja and other cities in Iraq's Sunni north and west where anti-US fighters are strongest.
Iraqi police also found two bodies dumped in the Sunni city of Baiji, 180km north of the capital.
One of the men had been shot in the head and the other killed by hanging, police said. Both had their arms tied behind their backs.
They have not been identified and the motives for the murders, which have become increasingly common in Iraq over the course of the year, were not known.
Fighters may try and disrupt
elections planned for January
At Dakkuk, near the northern oil centre of Kirkuk, one national guard was killed and three wounded when gunmen fired on their checkpoint early on Saturday.
In Mosul, Iraq's third city, 390km north of Baghdad, a civilian was killed and eight wounded when a bus was caught in the crossfire after a roadside bomb struck a US patrol, witnesses and hospital officials said.