The officials said on 10 November that Hatem al-Hassani was detained on 8 November.
His brother, Iraqi Parliament speaker Hajim al-Hassani, a moderate Sunni Arab, is running in the 15 December legislative elections on a secular list.
Rizgar Ali, the head of the Kirkuk city council, said Iraqi police arrested Hatem al-Hassani two days ago because he is the emir of a terrorist group.
He gave no further details. Kirkuk has seen violent confrontation among Sunni Arabs and ethnic Kurdish and Turkmen populations.
Earlier, police in Kirkuk said Hatem al-Hassani had been kidnapped, but later denied the account.