The 25-year-old Welsh light-heavyweight had been scheduled to defend his belt at London's Royal Albert Hall on April 28.
He said: "I've been unable to train because I've been laid up in bed and there's not enough time to make up what I've missed to make sure I'm fully fit.
"I've taken the advice of my doctor and been told to fully rest before attempting to start training again.
"I'm really disappointed because I was looking forward to being the first fighter to bring boxing back to the Royal Albert Hall in over a decade and the first of the century."
Cleverly, who is unbeaten in 24 fights, will be replaced by Billy Joe Saunders as the headline attraction at the London event.