The fight, which was a rematch of their 2011 encounter at Wembley Arena, had been due to take place at the Manchester Arena this Saturday.
The 30-year-old said: "I can't tell you how disappointed I am to have to pull out of the fight against Fury.
"I was in fantastic shape and had a great training camp, probably the best so far in my career, and was looking forward to getting revenge on Fury, but that will have wait.
"It is on the advice of my specialist that I have to do this. I'm sorry for the fans who will get to miss this great fight between me and Tyson but once my hand is healed and I'm given the all-clear to train and punch again, I'll be working on the new date for the fight."
The promoters confirmed that the event will be rescheduled once Chisora has recovered from the injury.