Six more people were wounded in the attack.
Reportedly an Egyptian official said the attacker was a former employee who had been fired from the restaurant in the Agouza area in the centre of the city.
Earlier reports had put the number of dead at 18.
The Middle East News Agency, quoting an unnamed security official, said three men on a motorcycle threw firebombs into the venue.
The fire was reportedly extinguished quickly and security authorities are investigating the attack.
Victims of the blast were burned to death or died from smoke inhalation. The restaurant, also a nightclub, was located in a basement, offering no escape route, the officials said.