However, Iraqi police told Muhammad Faeq, Al Jazeera's correspondent in Arbil that 20 people were injured in the explosion.
He also said that there were conflicting reports on the details of the explosion.
The cafe was located in a religiously and ethnically mixed town of Turkmen and Shia residents.
The bomber was wearing a belt filled with explosives and blew himself up at the cafe, police said.
But Kurdish sources told Al Jazeera that an explosive device planted on the side of the road near the cafe had detonated.
Meanwhile in west Baghdad, at least nine people have reportedly been killed by a car bomb, followed by clashes between fighters and security forces.
Medical and security officals also said that at least 19 people were wounded.
The attack came a day after the Islamic State in Iraq, an al-Qaeda-led group, announced a new phase of attacks during Ramadan.
On Saturday, a suicide car bomber killed at least 10 people and wounded 15 in southwest Baghdad as people were queueing outside the bakery in Al-Amil.
A resident in the Shia neighbourhood said there was no security checkpoint nor police stationed in the neighbourhood.
At least 34 people have been killed by bomb blasts and gunfire in Iraq since the start of the holy month of Ramadan on Thursday.