The fire occurred when a lighted candle, which was part of the stage set, fell on the floor at the theater during the performance of Shakespeare's play "Hamlet."
The fire quickly engulfed the wallpaper on the stage and spread to the theater, triggering a stampede by spectators and performers.
Theater Director Mustafa Alawi said there were about 100 spectators in the theater at the time of the accident, and that police were investigating the building to see why fire safety measures were not in effect.
Medical sources at the local hospital said many bodies were burned beyond recognition and that 14 of the injured suffered serious burns.
Bani Sweif is located some 100 kilometers (62 miles) south of Cairo.