There was no immediate claim of responsibility for the attack, but Ali al-Dabbagh, an Iraqi government spokesman, blamed al-Qaeda.
"Their ideology is to kill as much as they can from the Iraqi people," he told Al Jazeera. "Their ideology is just killing and that is why they are looking for soft places to have such attacks which we have on our citizens."
The attack came as the US military announced that 12,000 troops would be pulled out of Iraq by the end of September.
Major-General David Perkins, a US military spokesman, said on Sunday that violence had dropped more than 90 per cent and was at its lowest level since the summer of 2003.
"It's indicative that al-Qaeda feels threatened," he said of the attack. "They're feeling desperate. They want very much to maintain relevance."
Haitham Fadhel told The Associated Press news agenmcy that said he was standing in one of three lines of recruits arriving for their first day of special guard training courses at the academy when the bomber struck.
"We were feeling secure as we were waiting in a well-guarded area," he said.
"Before the explosion occurred I heard a loud shout saying 'Stop, stop, where are you going?' Seconds later, a huge explosion shook the area."
The Baghdad academy has come under attack before.
Fifteen people died and more than 45 others were wounded in two blasts on December 1, as groups opposed to the Iraqi government began to target security installations and employees around the country.
Security had been stepped up at the Baghdad academy to try to prevent further attacks and access to the building is intended to be only on foot through checkpoints.
Men are obliged to open their shirts to show they are not carrying weapons or explosives as they approach.
Palestine Street had been closed to vehicles for security reasons for two years. However one lane reopened late last year, though no stopping was allowed.