Police said the man was being held over alleged offensive behaviour. He is understood to be among those pictured in a recent police CCTV images appeal.
Several appeals for information were made after toilets were vandalised at the game and offensive effigies of Rangers fans were hung from the stands.
The match, which Celtic won 5-1, took place at Celtic Park on 10 September.

After 11 hours of secret discussions, the musicians could not reach a decision on a replacement for Sir Simon Rattle, who steps down in 2018.
Board member Peter Riegelbauer said they would try again "within a year".
The orchestra's 123 members met in a south-west Berlin church on Monday and were banned from using mobile phones.
But after an announcement was delayed several times, Mr Riegelbauer said: "I must unfortunately tell you that we haven't reached any result."
From September 2017, Sir Simon is to join the London Symphony Orchestra as its music director.
Among his possible successors are:
The Berlin Philharmonic, founded in 1882, has had three chief conductors over the past six decades:

Burnley Empire Theatre defaulted to the care of the Duchy of Lancaster as an "owner of last resort" after the ownership could not be established.
Last used as a bingo hall in 1995, the Cow Lane venue was recently named the fifth most at risk theatre in the UK.
Campaigners who want to restore the building to its former glory said the decision was a blow to their plans.
Sophie Gibson from the Burnley Empire Theatre Trust (BETT), said: "This news came as something of a surprise and a disappointment.
"The viability study, which the council contributed to as well, is currently taking place and the results are due very shortly.
"If, as we hope, the verdict is a positive one we can then move on to stage two, the architectural planning phase for the project, when we also begin applying for funding.
"All of this could have been for nothing if it is auctioned off before we are able to get that far."
The Duchy of Lancaster, said it had been left with "no alternative" but to put it to bidders after offering it free of charge to both Burnley Council and the Theatre Trust - an offer that "remains open".
A spokesman added: "The Duchy remains hopeful that the building will remain in local ownership."
BETT said it could not yet afford the legal costs that would be incurred to take on the building.
The four-storey building, designed by  G. B. Rawcliffe, opened in 1894 as a music hall, before being converted to a cinema in 1938.
It is to be auctioned in Manchester on 16 October.
A 23-year-old man has been arrested in connection with disorder at the recent Celtic v Rangers game in Glasgow.
[NEXT_CONCEPT]
Members of the Berlin Philharmonic orchestra have been unable to agree on who should be their next chief conductor and artistic director.
[NEXT_CONCEPT]
A dilapidated Grade-II listed theatre, which has stood empty for over 20 years, is to be sold at auction.