Mahmoud Basir, a witness, said: "The fire went on for about 20 minutes and went on to a hotel nearby until the fire fighters managed to put it out".
The theatre was scheduled to hold poetry recitations that night, but the fire had started just before the sunset evening meal during Ramadan, the Islamic month of fasting.
The theatre was opened in 1935 and had been recently renovated.
Zaki Tulaymat, an Egyptian sent by his government to study theatre in France, directed the performance of its first production, People of the Cave.
The theatre was a repository for artistic heritage and staged at least 820 performances since its debut.