The bombing took place on Wednesday as a crowd of Iraqis waited outside the centre to join the police force.
In Baghdad, four college students were shot dead by fighters who set up a checkpoint in the al-Dura area of the city, an unnamed interior ministry official said.
Also on Wednesday, Iraqi police discovered the bodies of 14 men near Baghdad's main amusement park.
The men had been handcuffed and tied up before being shot in the head, police said.
Hundreds of bodies have been discovered across Iraq in recent months, apparently part of a wave of sectarian violence between Sunni and Shia Muslims that has ripped through the country since the bombing of a Shia shrine in February.
The US military has said that 10 civilians were killed in Tuesday's suicide attack on a convoy carrying the governor of Anbar province, Mammun Sami Rashid.
Five of the governor's bodyguards were wounded in the attack.
Rashid told the military it was the 29th attempt on his life.
"This is a cowardly attempt, and this is not in the best interest of Anbar or the country," a US military statement quoted Rashid as saying.