The attacker got off the motorcycle rickshaw in the middle of Mraidi market and managed to escape before the bomb was set off, he said.
The attack comes a few days after US combat troops handed over the neighbourhood to Iraqi forces.
US troops plan to pull out of Iraqi cities, towns and villages by June 30.
Violence has dropped markedly in Iraq in recent months, with May seeing the lowest Iraqi death toll since the 2003 invasion.
But attacks remain common, particularly in Baghdad and the main northern city of Mosul.
Nuri al-Maliki, the prime minister, warned earlier this month that attacks were likely to increase in the coming weeks in a bid to undermine confidence in the Iraqi security forces.