Six arrests were made in the ground, with another three immediately outside.
A spokesperson for Strathclyde Police added that all arrests were for “minor offences” such as being drunk inside the stadium and breach of the peace.
Yesterday’s final derby of the season saw Rangers and Celtic draw 0-0.
Police had predicted a surge in violence over the weekend and an extra 1,000 officers were deployed to the streets.
Meanwhile, detectives hunting whoever sent parcel bombs to Celtic manager Neil Lennon and two others appealed for a couple to come forward as they may have “vital” information.
The man and woman were seen getting onto a bus near to where one of the packages was posted.
Detective Chief Superintendent John Mitchell, Head of Crime Division, said: “Although we have had good support from the public throughout this investigation, I am in no doubt that there are still people out there with vital information regarding this crime who, for whatever reason, have still not come forward to police.
“I am again re-appealing to anyone with any information, no matter how insignificant it may seem to them, to contact us. Please let us decide whether that information is important to our inquiries and take the appropriate action.”
A major police investigation is under way to trace whoever sent two packages to Lennon and one each to high-profile Celtic supporters Paul McBride QC and former MSP Trish Godman in recent weeks.
Police are trying to trace a young man and woman who were seen in the street at about 2.10pm that day getting on a Stagecoach number 20 bus which travels to Ardrossan.
The man is described as white, in his early 20s with dark hair. He was wearing a distinctive light blue and white top, and jeans.
The woman is described as white and in her early 20s, wearing a dark- coloured padded jacket.
Police are also trying to trace another couple, thought to be in their late teens, and a man who were seen separately walking their dogs near the post box on Montgomerie Terrace about 2pm on Friday April 15.
Lennon said the threats would not stop him from managing the Parkhead club.
He said: “I’ve had this for 10 years but I don’t want to say you get used to it, because you never do.
“But it is not going to deter me from doing what I want to do.”