A police source said on Thursday that the car bombs exploded just outside the heavily guarded ministry in central Baghdad.
Later in the day, a car bomber blew himself up near the local headquarters of the National Guard in the northern Iraqi city of Baquba, killing at least one civilian and wounding 14 people, a police official said.
The town's police chief was among those wounded, the official said.
Fighters frequently have attacked police and security forces in Baquba, 65km north of Baghdad.
Meanwhile, two Iraqis working for a construction equipment company that supplies American contractors were killed by fighters in Kirkuk, police said.
Fighters also targeted energy infrastructure, blowing up a gas pipeline feeding Iraq's main power station on Thursday.
The blast near Kirkuk forced two of four turbines at the Baiji power station to shut, engineer Khalid al-Lami said.