The 32-year-old was due to make his comeback to the ring in Manchester, with the eventual goal of taking on a Klistchko brother for a world title.
Fans who booked tickets for the Manchester Arena showdown will now be entitled to refunds.
Haye, the former WBA champion, said: "I’m absolutely gutted to have to pull out of this fight.
"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 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."