Amazingly the club captain completed the game at Ashton Gate on Saturday despite the injury.
Carey underwent tests over the weekend and is set to see a specialist later this week.
"Louis is obviously gutted but he is alright in himself and is home now," said City physio Nick Dawes.
"He played on through the injury and was seemingly happy after the game but we felt it was important he was checked out as a precaution. Unfortunately those x-rays showed up a fracture."
Manager Keith Millen added: "It is very disappointing, we are going to be without him for some time. It is important we allow him that time to recover."
Source: PA
Source: PA