The riot started ahead of the match between Egyptian Premier League clubs Zamalek and ENPPI.
According to security officials, clashes started when Zamalek fans, known as "White Knights," tried to enter the stadium without tickets.
Zamalek fans, however, denied the allegations and said on their group's official Facebook page that violence erupted after authorities only allowed entrance through one, barbed-wire door.
They said the narrow entrance to the stadium led to pushing and eventual clashes with police officers who fired tear gas to disperse the fans.
Speaking to AP News, a fan who chose to remain unidentified, said the stampede was a result of police firing tear gas at the crowd.
"Those who fell down could not get back up again," said the fan.
Egypt's public prosecutor said in a statement that an investigation to determine what caused the violence is underway.
Egypt's football fans are known to routinely clash with police inside and outside stadiums.
Regarded as deeply politicized, hardcore Egyptian football fans also played a major role in overthrowing former President Hosni Mubarak in 2011.
Following a February 2012 football match in Port Said, 74 people were killed in what is said to be the deadliest riot in Egypt's soccer history.
Following the violence, two police officers received a 15-year jail sentence for gross negligence and failure to stop the killings.