The Dutch giants fired Sven Mislintat with immediate effect after the ‘De Klassieker’ derby was called off in the 56th minute.
Home supporters threw flares and fireworks onto the pitch, with Feyenoord 3-0 up at the time, as trouble continued between fans and police outside the stadium late into the evening.
In a statement, the club said: “Ajax has ended the collaboration with Director of Football Sven Mislintat with immediate effect. The lack of broad support within the organisation is the reason behind this decision.”
The game at the Johan Cruyff Arena had already been paused twice, after fans had thrown plastic cups and fireworks onto the pitch, before a third offence led to the game being called off completely.
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A spokesperson for Ajax said: “This type of behaviour is not a part of Ajax.
"Ajax's management and supervisory board distance themselves from the misconduct that led to the suspension of the match against Feyenoord and the disturbances afterwards.
"Disappointment about the season's poor start is understandable but can never be the cause of disorderly conduct. We apologise to everyone who has felt unsafe or has been affected in any other way."
Ajax have started this season poorly, winning just one of their first fourleague games and sitting 13th in the Eredivisie, two points above the relegation places.
Maurice Steijn’s side finished third last season and failed to qualify for the Champions League for the first time in 13 seasons.
Instead, Ajax are in the Europa League this term - being drawn in Group B alongside Brighton, Marseille and AEK Athens.
Brighton first face Ajax at the Amex Stadium on October 26 and then travel to the Netherlands for the return game on November 9.