The attackers tossed multiple Molotov cocktails inside the establishment located at a hotel in the Agouza area near the center of Cairo in the early morning assault, starting a fire, Egyptian media reported.
The Cairo Post newspaper says three masked assailants reportedly carried out the attack.
Six people were injured, according to preliminary estimates.
Cairo police are searching for the perpetrators as a rescue operation continues. An official told Reuters that one of the suspects was an employee of the restaurant that was attacked.
The restaurant/nightclub is in the basement of the hotel building, with few escape routes. The firebombing turned it into a death trap for patrons and employees. The victims burned to death or died from smoke inhalation.
Security remains an issue in Egypt as Islamist militants conduct attacks mostly targeting security troops after the military deposed Islamist President Mohamed Morsi of the Muslim Brotherhood following 2013 mass protests.