Costa Rican Esteban appeared to retaliate against the fan after being kicked himself.
After he was dismissed Alkmaar coach Gert Jan Verbeek ordered his team to leave the pitch and the match was called off with Ajax leading 1-0.
"Verbeek ordered the team off the pitch to control the situation and in the dressing room our players said that they don't feel safe anymore on the pitch," said Alkmaar's technical director Earnest Stewart.
Ajax official Jeroep Slop said that the police arrested a 19-year-old man.
"I saw that Esteban was attacked and that he defended himself," said Ajax coach Frank de Boer.
"Don't know how I would have reacted but I can understand Esteban with his South American temper."
"I understand the decision of Alkmaar because of all the emotion at that moment."
Alkmaar director Toon Gebrands said that the club would respect any decision taken by the disciplinary board of the Dutch Football Association (KNVB) but that the safety of his players was at stake.
In other action on Wednesday Heerenveen thrashed second division side FC Top Oss 11-1.
NEC Nijmegen cruised to a 3-0 win over the amateurs of Achilles 29 Groesbeek.
On Thursday Twente Enschede host PSV Eindhoven for a place in the quarter-finals.
