The match has been classed in Category A as it will be televised by Sky Sports at 4pm which means the Gunners would charge £62 per ticket.
But City have sent back 912 of the 3,000 tickets allocated because the cost of attending for a lot of supporters is far too high.
"It's the most expensive amount I can ever remember paying for a ticket in my life, for a Sunday afternoon game which is live on satellite television," general secretary of the Manchester City Supporters Club, Kevin Parker, told The Guardian.
"And it's not as if finding a television to watch the game on is difficult nowadays. Even if the game wasn't live, to charge £62 to watch it is ridiculous, but to charge that amount when people can see it live on TV is crazy.
"It just shows that football clubs are out of touch with reality. If City supporters are travelling on a supporters' club coach it will cost £30 per person. That's £92 before they have even done anything; add in a programme, food, drink and you are looking at £125-£130 per person.
"There are a combination of things at play here. Some people cannot afford the price, especially as it is just after Christmas, and there are some who just refuse to pay £62. This is also the first time in a long while that I remember City fans saying to me they could pay the money but are refusing to do so.
"That is a brave decision to take. Soon, though, fans will vote more strongly with their feet and clubs like Arsenal will have to decide what to do about ticket prices."