The alert Costa Rican goalkeeper Esteban Alvarado deflected the attack by a 19-year-old fan, tripping him with a karate-like kick. But Alvarado was given a red card for kicking the supporter again in anger twice immediately afterward before the intruder was dragged off by security guards.
Alkmaar coach Gertjan Verbeek ordered his side to walk out in protest rather than play with 10 men and the game was halted in the 36th minute. Ajax were leading 1-0 after a goal by Gregory van der Wiel.
Ajax director Jeroen Slop said the supporter had already been banned from the stadium for a year due to a previous run-in with security guards, but managed to sneak into the cup match with a ticket purchased by a friend. He has now received a lifetime ban from all Ajax matches.
Later on Thursday, the Dutch football association rescinded the red card, saying Alvarado's reaction was triggered by the unprovoked attack on him - but adding that referee Bas Nijhuis was acting according to the rules when he sent the goalkeeper off.
The federation said Alvarado's reaction "will not result in a ban."
Opinions were divided about whether Alvarado deserved to be sent off in the first place.
Nijhuis defended the decision, saying that once the supporter was on the ground, he no longer posed a threat.
But Ajax coach Frank de Boer noted that for all Alvarado knew, the supporter could have been carrying a weapon or gotten up to attack again.
"Maybe I would have done the same thing, maybe not," said De Boer, a renowned former defender for Netherlands' national team, of Alvarado's reaction. "But emotionally I do understand it."
The Dutch players' union had demanded that the red card be retracted.
"This cannot lead to a suspension" for Alvarado, said union chief Danny Hesp, arguing that Alvarado's reaction was in self-defense after an unexpected, unprovoked attack. The union "will do everything it can to fight this" decision, he said.
The federation said on Thursday it will decide "soon" whether Wednesday's match should be replayed, resumed, or have Ajax declared the winner.
Police are holding the 19-year-old supporter, whose name was not released, on assault charges. Police are also holding 25 other supporters arrested during and after the match. After the early end to the round-of-16 match, Ajax supporters clashed with riot police outside Amsterdam's Arena stadium.
Alkmaar defended their decision not to continue playing. The team's players "didn't feel safe anymore in this situation," said club director Toon Gerbrands.
In a highly unusual move, the country's justice minister Ivo Opstelten got involved in the debate, saying the attack was "beastly" and that "jerks and nuts don't belong on the field." He added that he thought AZ's Verbeek was right to walk out under the circumstances.
"I have a lot of respect for how he acted," Opstelten said. "Intervene immediately, that warms my heart."
Slop, the Ajax director, apologised for the security lapse, and he said AZ had accepted the apology.
"An incident with one half-wit in a stadium of 40 000 people, you don't have control over that," he said. He said the supporter had "in all likelihood been drinking."
He added that the fan "had made it known that he detests the AZ keeper and that's why he attacked him."
Esteban Alvarado kicks a soccer fan. (Photo: Associated Press)