The Amsterdam club brought 2600 fans to Glasgow for their Champions League defeat earlier this month.
But a section of their supporters let themselves down by ripping up seats and flinging them at police and stewards.
Celtic have informed the Dutch champions they will need to fork out for replacing the damaged seats in the stadium.
A spokesman for Ajax said: "We have been advised the bill from Celtic will be £25,000.
"We also have to wait and see what comes out of the investigation from Uefa.
"We want to recover these costs from the fans who were actually guilty of this destruction.
"We hope that the footage from the game will point out the perpetrators."