The incident comes just two days after the press conference was held in the UK for the scheduled encounter in Dusseldorf, Germany on October 24.
Following previous bouts with ex-WBA champion David Haye collapsing, Fury has now missed out on three high-profile contests due to no fault of his own.
Fury, 27, had dressed as Batman for an entertaining press conference on Wednesday and gave Klitschko a piece of his mind, only to be disappointed before the events had time to sink in.
An ex-British, Commonwealth and European title holder, Fury is yet to taste defeat as a professional and earned his chance with victories over Dereck Chisora and Christian Hammer.
It was reported in German press source Bild.de that Klitschko damaged a tendon in his left calf during preparations and needs recovery time before getting back into camp.
The 40 year-old currently holds the WBA, WBO, IBF and IBO titles and was due to face Fury as his mandatory challenger at the ESPRIT Arena.
An announcement on how long the Ukrainian will be out of action is set to be made in the near future.
