The Parkhead club defeated Hibs 2-0 on Saturday evening to book themselves a place in the semi-finals of the Scottish Cup as they chase a historic treble treble.
Damaged seats in the away end were visible after the jubilant crowd had exited the stadium. There is an agreement in place between top flight clubs that covers any damage at away grounds.
Celtic were hit with a similar bill after their 1-0 victory over Kilmarnock in the Ladbrokes Premiership last month.
Saturday’s match was marred by off-the-field incidents as Celtic attacker Scott Sinclair had a Buckfast bottle thrown at him during the game.
Hibs also reported objects being thrown from the away end during the contest.