After just 55 minutes of the Eredivisie fixture, the referee opted to halt the game amid anger from the home supporters.
Ajax, who are 36-time Dutch champions, have endured a dreadful start to the season, picking up just one win from four outings in the league.
They hosted rivals Feyenoord on Sunday in De Klassieker at the Johan Cruyff Arena but fell 3-0 down before half-time.
A double from Santiago Gimenez and Igor Paixao's strike were enough to send the unbeaten visitors into a commanding lead.
The match was initially halted before half-time as fireworks were thrown onto the pitch.
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Play then resumed and after ten minutes of stoppage time, both sides went into the tunnel at the break.
However, the same thing happened again and the match was officially suspended.
Videos on social media then showed some supporters trying to storm their own stadium after the match was suspended.
Riot police on horses could also been seen outside the ground amongst a sea of angry fans, who had tear gas to disperse on some occasions.
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Boss Maurice Steijn has come under scrutiny in recent weeks amid such results, as well as director of football Sven Mislintat.
The Dutch giants appear to be in crisis and such a performance against their rivals has not helped matters at all.
It remains to be seen if the match will resume as fans express their anger at the club.