After Klaassen put Ajax 2-1 up, a confrontation between rival players near the corner flag set off a commotion, during which the Netherlands midfielder was hit on the head, seemingly by a cigarette lighter.
Ajax players walked off the field, followed by those of Feyenoord, whose assistant coach John de Wolf later came out to berate home supporters before the game got back underway.
He used the public address system to ask Feyenoord fans to "use your common sense".
The incident forced the game to be halted for 28 minutes and Klaassen had to be substituted shortly after the game resumed, gesturing that he was suffering from dizziness.
"I had a throbbing feeling around the wound and I also had trouble focussing, so I could have stayed on the pitch but that was not going to help me nor the team," Klaassen told the Ajax website.
"It was hard... you don't want to let it get to you but sometimes you have to put your pride aside and do what's best for the team."
Police said a 32-year-man had been arrested and the incident was being investigated.
The match had started five minutes late due to smoke from fireworks lit by Feyenoord supporters. It had to be stopped 21 seconds after kick-off to allow the heavy black smoke to clear.
