When flares were thrown onto the pitch for a second time, with many landing near the goal, the referee stopped the contest and directed the players down the tunnel.
Fans paid no heed as the club displayed the message "Lighting of fireworks is prohibited" on the big screen at the Johan Cruyff Arena in Amsterdam.
"One of the most important games in the Netherlands is discontinued," interim Ajax chief executive Jan van Halst said. "That's serious. Everyone is angry and sad because of this.
"The most important thing for now is that everyone -- guests and supporters -- safely leave the Johan Cruiff Arena. For now things seem to be going well. But we're still try to manage the situation.
"We understand the disappointment among supporters. We have a really bad start of the season. There is a lot going on around our club. But, that is no reason for this actions. We strongly disapprove this. The measures we take in the Netherlands do evidently not work. Not enough."
Fans paid no heed as the club displayed the message "Lighting of fireworks is prohibited" on the big screen at the Johan Cruyff Arena.
"De Klassieker has been permanently suspended after repeated fireworks on the field," Eredivisie said in a statement. "More information on playing out this game will follow later."
Feyenoord manager Arne Slot said it was "especially annoying" that his side were not able to finish what had been a superb performance.
"In this way the chance for something very beautiful is taken away from us," he said on the club website. "We understand the decision that has been taken, but we do not feel a sense of victory... And so we certainly won't get on the bus satisfied."
Ajax, who have had a poor start to the season with just one win, sit 13th in the 18-team league. They conceded all three goals on Sunday in the first half, leading to discontent from the fans.
The club finished third last season and failed to qualify for the Champions League for the first time in 13 seasons. They had finished champions seven times and runners-up another five over the previous 12 seasons.
Sunday's derby becomes the latest to be abandoned in Dutch football, which has struggled to deal with fan behaviour in recent years.
The Dutch football federation (KNVB) instituted a rule that suspends any match for 10 minutes after an object is thrown by fans onto the field. Once a match has been restarted for a second time, any further objects thrown will cause the match to be abandoned.
Caretaker Dutch Justice Minister Dilan Yesilgöz-Zegerius said in a message on X, formerly Twitter: "This no longer has anything to do with football and being a supporter. You play with the safety of the players, fellow supporters and yourself. Shame on you!"
Later on Sunday, Ajax announced they had parted ways with their director of football Sven Mislintat with immediate effect.
In May, Ajax appointed Mislintat as the successor to Marc Overmars, but the association proved to be shortlived.
"Several attempts to restore broad support have not led to the desired outcome. This leads to unrest in and around the club, also due to the disappointing results," Ajax interim Van Halst said in a statement.
Information from The Associated Press was used in this report.