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The former WBA heavyweight champion was scheduled to fight Charr in Manchester on June 29.
Haye announced his withdrawal in London, two days after suffering the injury.
The damage to his left hand occurred on Sunday evening and left the former WBA heavyweight champion with no option but to postpone his return to the ring. He said the hand would need at least four weeks of rest.
The controversial British fighter announced recently that he would fight the Lebanon-born German, who also has Syrian heritage, in his comeback bout.
Haye has fought only once since losing his WBA title to Wladimir Klitschko in July 2011. He knocked out Dereck Chisora in July last year.
"I'm absolutely gutted to have to pull
out of this fight on June 29," he said. "I pick up injuries now and
again in training, and sometimes carry them into fights, but this was one I
simply couldn't recover from in time. I need to rest it up for at least four
weeks.
"I apologise to Manuel Charr and to everybody involved with the promotion. But most of all I want to say sorry to the thousands of fans who bought tickets to the fight.
"I felt it was important to let them know about the cancellation as soon as possible, so they can now make other plans.
"As soon as I am told I can resume full training, my loyal fans will be the first to know."
Charr twice challenged Haye to a fight after both lost “world” title bouts to one of the Klitschko brothers over the past 18 months.
Haye he won 26 and lost two of his professional bouts. Charr has a record of 23 wins and one defeat.
The 28-year-old Haye’s return would have been televised live and promoted as part of a new relationship between Adam Booth of Hayemaker and Eddie Hearn of Matchroom Sport.
Haye was looking for another shot at one of the Ukrainian Klitschko brothers and believed a victory over Charr would have put him back in line for a title fight.
WBA, IBF and WBO champion Wladimir beat Haye on points in July 2011. His older brother Vitali, the WBC champion, stopped Charr in September last year.
