Police Scotland said they were aware of the damage but that Celtic FC were dealing with the situation as an internal matter.
Celtic beat Rangers 5-1 after Moussa Dembele scored a hat-trick.
One man was arrested for an alcohol-related offence.
Pictures of the vandalism showed toilets in the ground were wrecked.
Ch Supt Brian McInulty said: “I would like to thank all the supporters who came to enjoy the match today in a safe and responsible manner.
“You listened to what we asked and behaved accordingly which has helped our officers ensure the safety of everyone attending the venue.
“All fans came out to enjoy the match and soak up the atmosphere and this is what football should be all about.
“I sincerely hope that the good spirits of both sets of supporters continues throughout the rest of the day and the rest of the evening.”