After scoring the goal to put Ajax 2-1 ahead at De Kuip, Klaassen was hit on the head by an object thrown from the stands, leaving him with a nasty cut.
The referee decided to take the players off the pitch due to safety fears and the game was halted for almost half an hour.
The game only restarted following a plea from Feyenoord assistant John de Wolf, telling the home support very bluntly that no objects should be thrown onto the field of play.
Fireworks being set off by the home fans had already delayed the kick-off earlier in the evening, meaning the match went on until almost 11pm local time.
After the resumption of play, Ajax held onto their 2-1 lead to book a place in the final, where they will meet PSV Eindhoven.
A 32-year-old man has been arrested in connection with the attack on Klaassen.