The Canaries defender was diagnosed as having haemothorax, which is a build up of blood between the ribs and the lungs, which worsened after he took a knock to his ribs in the 1-1 draw at St Andrew's on Saturday.
Holt is being kept in hospital until early next week the club have confirmed and will be sidelined for a number of weeks as he looks to fully recover from the illness.
"Gary became very unwell after the game against Birmingham," club doctor Peter Harvey has told the clubs official website.
"He had complained for a few weeks of a recurrent pain in his ribs. This is a common complaint from footballers.
"He played on and trained hard, despite the fact he was in pain.
"I went to see him on Saturday after the game and found him to be quite unwell. It wasn't exactly clear what the trouble was.
"We looked at him again on Monday and he wasn't any better so we had him admitted to hospital."