The City keeper dislocated a shoulder in the second half of the 0-0 draw at The Emirates on Saturday evening and will not play again this season.
"Shay's injury will be a problem. It's not good for us because Shay is a fantastic goalkeeper," City boss Roberto Mancini said.
"He is important to us, but in football you can always get injured.
“I hope it’s a little injury, but I don’t know.
"Shay is in hospital, but we have ten days and must play three big games."