The former heavyweight world champion lost their first encounter in March after an 11th-round stoppage, picking up an Achilles problem during the bout.
And now Haye has pulled out of the fight on December 17 with an arm problem that needs surgery.
“I am devastated to announce my much-anticipated rematch against Tony Bellew has been postponed until March 24 or May 5, subject to scheduling,” said Haye.
“Despite the recent injury rumours, I was in perfect condition with an incredibly strong training camp, currently weighing lighter than I have for more than five years, I couldn’t wait to get back in the ring.
“I was ready to rewrite the ending of the Haye Bellew saga. “
“Unfortunately, after a freak accident during a stair conditioning session, which I’ve done with no incident hundreds of times, I lost my footing, slipped, so instinctively grabbed the bannister to stop myself toppling down the stairwell, in doing so I somehow managed to damage my bicep in the process.
“This afternoon 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 will be able to be back in the gym to start my arm rehabilitation in two weeks.
Bellew was also disappointed with the news. He said: “I’m gutted that the rematch with David has been postponed, both for myself but more for the fans. I’ve had a tough camp with a lot going on in my life but was ready to repeat my win from March.
A new date is set to be announced for early 2018.