The fight was due to be held on Oct. 29 in Manchester, having been originally postponed in July when Fury suffered an ankle injury.
"Tyson has this week been declared medically unfit to fight," his promoters Hennessy Sports said in a statement without elaborating.
"Medical specialists have advised that the condition is too severe to allow him to participate in the rematch and that he will require treatment before going back into the ring.
"We and Tyson wish to express our sincerest apologies to all those concerned with the event and all the boxing fans who had been looking forward to the rematch. Tyson is understandably devastated by the development," read the statement.
"We will be making a further statement in due course. Until then we ask that Tyson and his family be given the privacy and the space he needs to recover during this difficult time."
Previous champion Klitschko, who had ruled the heavyweight division for a decade, raised doubts about the fight going ahead during a news conference earlier this month.
Fury, who has been charged over anti-doping violations but denies any wrongdoing, caused a huge shock when he registered a unanimous points victory over the Ukrainian in Duesseldorf in November.
The unbeaten Briton, who has courted controversy throughout his career, was charged by UK Anti-Doping (UKAD) in June after a urine sample taken nine months before he beat Klitschko showed traces of the banned substance nandrolone.
Fury's legal team said the result of tests on the samples in March and May 2015 were contradictory and launched High Court proceedings against UKAD.
A provisional suspension was lifted pending the result of an independent hearing.
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
