The 39-year-old Klitschko's WBA, WBO, IBF and IBO crowns were to be on the line when the pair met in the German city of Duesseldorf on Oct. 24 but the Ukrainian sought medical treatment on Thursday after tearing a tendon in his calf.
"I was looking forward to this fight," Klitschko said in a statement.
"I am really sorry not to be able to box on Oct. 24 and that of course goes for my opponent as well who has been preparing for this fight for weeks. I will do everything possible to get fit as soon as possible."
A new date will be announced next week after further medical checks, with the location of the fight remaining Duesseldorf.
Klitschko has not lost for 11 years and has a record of 64 wins and three defeats, while the 26-year-old Fury is undefeated at 24-0.
(Reporting by Karolos Grohmann; editing by Clare Fallon)
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