As well as the arrests for violent disorder, one person was arrested for attacking a steward, five for drug offences and three for common assault.
Other arrests were over attempts to get into the game with a forged ticket and public order offences such as “tragedy chanting”, where fans sing about tragic events in the opposing team’s past.
Greater Manchester Police said the violence had taken place around 18:00, two hours before kick off.
Assistant Chief Constable Chris Sykes, match commander for the game, said the “vast majority” of fans had behaved well and been able to have a “safe and enjoyable time” at the game.
Manchester United said it had taken “the strictest possible measures” to prevent Rangers fans getting tickets in the home end, including only selling them to people who were registered on the club’s database before August, when the teams were drawn together.
A spokesperson added: “Whilst the unauthorised touting of tickets has become more difficult since our introduction of in-app digital ticketing, it cannot be completely eliminated.
“All examples of away fans in home areas will be investigated over the coming days, with the strongest possible sanctions taken against the registered holders.”
BBC Scotland News has approached Rangers for comment.
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