The riot, only three years after similar violence killed 74 people, began ahead of a match between Egyptian Premier League clubs Zamalek and ENPPI at the Air Defence Stadium east of Cairo.
Such attacks in the past have sparked days of protests pitting the country’s hardcore fans against police in a nation already on edge after years of turmoil.
Two security officials said at least 25 people were killed.
The violence comes as police face increasing scrutiny following the shooting death of a female protester in Cairo and the arrest of protesters under a law heavily restricting demonstrations.
President Abdel-Fattah el-Sissi has pledged to bring stability to Egypt amid bombings and attacks by Islamic militants, but also has said Egypt’s emergency situation meant that some violations of human rights were inevitable, if regrettable.
Egypt’s public prosecutor issued a statement ordering an investigation.
After convening an emergency meeting to discuss the violence, the Cabinet announced that it was postponing upcoming football matches until further notice, Egypt’s state television said.
What caused the violence was not immediately clear. Security officials said Zamalek fans tried to force their way into the ground without tickets, sparking clashes.
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Fans have only recently been allowed back at matches and the interior ministry planned to let only 10,000 fans into the stadium, which has a capacity of about 30,000, the officials said.
Zamalek fans, known as “White Knights,” posted on their group’s official Facebook page that the violence began because authorities only opened one narrow, barbed-wire door to let them in.
They said that sparked pushing and shoving that later saw police officers fire tear gas and birdshot.
A fan who tried to attend the game said the stampede was caused by police who fired tear gas at the tightly packed crowd.
“Those who fell down could not get back up again,” the man said.
The Zamalek fan group later posted pictures on Facebook it claimed were of dead fans, including the names of 22 people it said had been killed.
Egypt’s hardcore football fans, known as Ultras, frequently clash with police inside and outside of stadiums.
They are deeply politicised and many participated in the country’s 2011 uprising that forced out president Hosni Mubarak.
Many consider them as one of the most organised movements in Egypt after the Islamist Muslim Brotherhood, which the government outlawed as a terrorist organisation following the 2013 military overthrow of president Mohammed Morsi.
The deadliest riot in Egypt football history came during a 2012 match when Port Said’s Al-Masry team hosted Cairo’s Al-Ahly.
That riot, at the time the deadliest worldwide since 1996, killed 74 people, mostly Al-Ahly fans.
Two police officers later received 15-year prison sentences for gross negligence and failure to stop the Port Said killings, a rare incident of security officials being held responsible for deaths in the country.
Seven other officers were acquitted, angering football fans who wanted more police to be held accountable for the incident and other episodes of violence. In response, angry fans burned down the headquarters of Egypt’s Football Association.