The match had already been suspended twice during the first half, once for flares on pitch, the other time after a cup was lobbed from the stands.
A double from Santiago Gimenez and one from Igor Paixao had given the team from Rotterdam an unprecedented first-half lead at the Johan Cruyff Arena in Amsterdam.
TV images showed three flares burning on the pitch with smoke from other flares pouring from the notorious south stands of the arena, where the hardcore "F-side" fans sit.
According to Dutch media reports, police used horses and fired tear gas to disperse fans from outside the stadium. Images on social media showed fans attacking the entrance to the stadium.
The coaches and players were kept in the dressing rooms over fears for their safety.
Ajax have had a miserable start to the season. After winning their first match, they have drawn two and lost one in the Eredivisie. They currently sit 13th in the table.
The club is in chaos off the pitch as well, with technical director Sven Mislintat under investigation for potential conflict of interest over a recent transfer.
Defending champions Feyenoord, in contrast, remain unbeaten in the top flight this season.
"This has nothing to do with football and being a fan. You are playing with the safety of the players, fellow supporters and yourselves. Shame on you," said Justice Minister Dilan Yesilgöz - Zegerius on X, formerly known as Twitter.
Authorities in the Netherlands are battling a fresh surge in football violence, with around a dozen serious incidents last season.
In May, black-hooded AZ Alkmaar fans tried to storm the area reserved for friends and family of West Ham staff following the Hammers' 1-0 win in the Europa Conference League semi-finals.
At the time, West Ham manager David Moyes admitted he was concerned for the safety of his family, while stars from the Premier League team climbed over the hoardings in a bid to stop the trouble.
The 'Klassieker' is always a tense affair and last season, Ajax midfielder Davy Klaassen was injured on the head after a Feyenoord supporter tossed a lighter from the stands.
Several other games involving Dutch first division teams like FC Utrecht, FC Twente, Go Ahead Eagles, RKC Waalwijk and Sparta Rotterdam also had to be called off due to hooliganism.
One game, between Ajax and Groningen, lasted a mere nine minutes before being called off with smoke bombs raining down on the pitch.
