A city official told AFP news agency that militants had tried to seize the compound but were unsuccessful.
No group has said it carried out the attack.
Kirkuk is ethnically mixed, and at the centre of a dispute between the Iraqi government and Kurds over oil and land rights.
Two weeks ago at least 10 people were killed in a suicide bomb attack on the offices of the Kurdish Democratic Party in the city.
Sunni insurgents linked to al-Qaeda have been blamed for much of the recent violence in Iraq.
However, there has been a relative calm in recent days.
The attack took place during morning rush hour in the centre of Kirkuk, police Brig-Gen Natah Mohammed Sabr told AFP.
At least 70 people were injured as militants reportedly dressed in police uniforms and armed with guns, grenades and suicide vests rushed the main gate of the headquarters after a bomb was detonated.
They threw grenades but were killed before they reached the building of the headquarters.
The attack caused massive damage to nearby buildings, Brig-Gen Sabr added.
Traffic in the city centre was stopped, and offices in the area were evacuated.
With its massive oil reserves, Kirkuk is the most bitterly contested of Iraq’s disputed territories.
It houses a mixture of Arabs, Kurds and Turkmen.
The Kurds want to incorporate it into their largely autonomous region, while Arabs and Turkmen oppose any change to its current status, ruled directly from Baghdad.
Correspondents say militants often exploit differences between the Iraqi and Kurdish security forces by launching deadly attacks in the city.
9_WqUgVdIaoImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…