According to reports, Chisora's hand had been feeling sore over the weekend, and an MRI scan today revealed he has a broken bone.
The two were due to meet in a rematch of their 2011 collision, won by still-unbeaten Fury, in Manchester on July 26.
However the injury to Chisora means the fight will now be set for a later date.
The turn of events is similar to what happened to Fury's abandoned plans to clash with former world heavyweight champion David Haye last year - Haye withdrew with a bad cut from training a week before they were due to fight.
Haye-Fury was then permanently canned when Haye suffered another injury ahead of their February 2014 reschedule.
Recently on Twitter, Fury remarked:
"Don't even think of pulling out of this fight b**ch. Don't do a @mrdavidhaye & be a s**thouse c**t. You'll be a laughing stock."
Fury has been reprimanded for his foul language already during press conferences to hype the now-postponed bout.
Eddie Hearn, promoter of rival firm Matchroom Boxing, tweeted in reaction to the collapse of Frank Warren's big bout before hastily deleting.
Many believe the tweet was a dig related the rumours the bout was already under pressure due to poor ticket sales.
The build up to the fight, due to take place at the Phones 4 U Arena, had not generated as much interest as perhaps was expected.
It is doubtful if any of the planned undercard fights will now go ahead without the main event.
Billy Joe Saunders was due to fight Emanuele Blandamura for the European welterweight title, while Terry Flanagan was due to contest the British lightweight title against Martin Gethin.
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