Stalls and soft-drink stands were destroyed by the explosion. Two passers-by were killed and eight others wounded, a police official said.
Karrada, a predominantly Shia area in central Baghdad, had been relatively calm in recent weeks after the so-called US security crackdown in the capital.
The army recruits killed on Sunday were Sunni Arabs from the western Anbar province that had just joined the Iraqi security forces.
They had been at a recruitment centre in the town of Fallujah earlier in the day.
Tribal leaders in Anbar have rounded up thousands of young men to join local security forces.
The shift by tribal elders last year towards supporting the interim Iraqi government forces has sparked a power struggle with foreign and anti-government fighters in the province.
One day before, more than 150 people were killed by a lorry bomb in a crowded market in the northern Iraqi village of Amirli, an Iraqi military commander told Al Jazeera.
Many homes in the small community were destroyed on Saturday when a suicide bomber detonated a powerful bomb on a lorry loaded with bricks, security and administration officials said.
It was the second attack on a village in the north of the country in 24 hours. A suicide car bomber killed 22 people and wounded 17 others late on Friday when he drove his vehicle into a group of Shia Kurds near Iraq's border with Iran.