The 27-year-old is alleged to have committed the offence at Ibrox Stadium on Saturday and is being held in police custody.
A spokesman said: “Police Scotland can confirm that following an incident at the Rangers v Celtic match on Saturday April 29, a 27-year-old-man has been arrested and is presently detained in police custody in connection with an alleged offence under the Offensive Behaviour at Football and Threatening Communications Act.”
Police said it was the second arrest regarding behaviour of this type at the game.
A man was charged after allegedly making a monkey gesture towards Celtic player Scott Sinclair as he celebrated scoring the opening goal in Celtic’s 5-1 win over Rangers.
A 17-year-old woman has also been reported to the procurator fiscal over an alleged racist post on social media.
Police said the 27-year-old man will also be reported to the fiscal.