The Interior Ministry said that scores of thousands of fans stampeded to break into the gates of Air Defense Stadium.
The fans had no tickets, the ministry said in a statement.
They died of suffocation and stampede after being tear-gassed, the ministry added.
The fans blocked the roads outside the stadium.
The public prosecution was notified to launch an investigation into the incident.
Police used tear gas to disperse members of the Ultras White Knights in front the stadium before Zamalek played ENPPI in a top-of-the-table clash.
The death toll has reached 15 while 25 were injured.