Bellew stopped compatriot Haye in the 11th round when they met in March and the sold-out re-match was scheduled for Dec. 17. It will now be postponed until March or May.
Haye said he had suffered a bicep injury after falling while working out on the stairs.
"I am devastated to announce my much-anticipated rematch against Tony Bellew has been postponed until March 24th or May 5th 2018, subject to scheduling," said Haye.
"After a freak accident during a stair conditioning session, which I've done with no incident hundreds of times, I lost my footing and slipped," Haye said in a statement.
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"I instinctively grabbed the banister to stop myself toppling down the stairwell. In doing so I somehow managed to damage my biceps.
"I underwent a procedure to repair it; this was pretty straightforward and my doctor and physiotherapist have no doubt that not only will I make a full recovery but (I) will be able to be back in the gym to start my arm rehabilitation in two weeks," said the 37-year-old.
"I would like to apologise to Tony, his family and his training team, as well as all our fans who have been left disappointed," he added.
Following the news another British fighter, former world heavyweight champion Tyson Fury, said he would relish the chance to fight Bellew. Fury is hoping to return to the ring next year once a UK Anti-Doping hearing has been concluded.
(Reporting by Simon Evans; editing by Ken Ferris)
