The evening attack struck inside the cafe in the Washash neighbourhood, a police officer and a medical source said, leaving at least 12 others wounded.
The blast was a rare bombing in recent days in the Iraqi capital, which has endured a tense calm as security forces and militants have focused their resources north and west of Baghdad, with a militant-led offensive having overrun swathes of five provinces.
Iraqi forces initially wilted when faced with the insurgent onslaught, which began late on June 9, but have since performed more capably, albeit with few gains in offensive operations.
The militant advance displaced hundreds of thousands of people, alarmed the international community and heaped pressure on incumbent Prime Minister Nuri al-Maliki as he seeks a third term in office following April elections.
The offensive was led by the Islamic State (IS) militant group, whose leader Abu Bakr al-Baghdadi, delivering a sermon at a mosque in Mosul, the first city to fall in the militant onslaught.