Neither was at the offices at the time of the explosion.
The car bomber turned off the main road and accelerated towards the checkpoint where the morning shift guards were gathered, Iraqi police said.
Also on Tuesday, the US command in Iraq announced that a US soldier had died of his wounds sustained when a suicide bomber blew up a car near the soldier's convoy in Salaheddin province north of Baghdad.
Two other soldiers were wounded in the blast, which occurred on Monday.
Monday saw at least two major attacks in separate areas of Iraq.
An explosive fire erupted in a storage tank at Baghdad's only oil refinery, sending smoke and flames high above the capital.
The US military said an "industrial accident" caused the fire at the Dora refinery in Baghdad.
But Brigadier Qassim al-Moussawi, the chief Iraqi military spokesman, said that a rocket struck a storage tank, triggering the blaze.
In the second attack, mortar shells crashed into an Iraqi prison at a major government complex, landing in a cellblock and killing at least five inmates.
Iraqi police and hospital officials said seven inmates were killed and 23 more wounded when the mortar rounds hit the jail, which held prisoners accused of terrorism-related crimes or civil offences.
The US military said five people died and another 25 were injured.
Police said US troops sealed off the area around the main interior ministry compound on the east bank of the Tigris river in central Baghdad.
In other news, Hoshyar Zebari, the Iraqi foreign minister, said a new security pact with the US would set a time limit on the American troop presence.
He said the government's goal was "to reach a level of preparedness" that removes the need for foreign forces.
Iraq formally requested UN authorisation for the US-led presence in Iraq, he said.
Meanwhile, Iraqi officials said Nuri al-Maliki's government was putting together a committee to study possible pardons for several people convicted of offences as a move towards national reconciliation.
Sadiq al-Rikabi, an adviser to the prime minister, said a major task of the new committee would be to determine whether some offences cannot be pardoned under the Iraqi constitution, namely those involving mass killings or financial corruption.
Some may require parliamentary approval while others could be done by the government on its own, he said.