Promoters were hoping to book the heavyweight collision between Fury and Usyk in December, with the fight expected to be held in Saudi Arabia.
However, since beating Anthony Joshua for the second time, Usyk revealed he is nursing old injuries and has no desire of returning to the boxing ring in December.
Fury hit back on social media, saying in a video: "Usyk. Middleweight. You say you want the WBC [title], and it's held by gypsies. It is held by the Gypsy King. And it's held tightly, grasp tight.
"And all the roads lead to a seven-foot behemoth that will absolutely destroy you, middleweight.
"Middleweight. You will get smashed to bits. You say you wanted to fight me after beating the body builder. Call me out on television. Now you're being a little b***h. P***y boy.
"Running, hiding. Saying you've got injuries. You ain't got no injuries, you had a sparring contest.
"Get out, fight, December. Let your mouth go, see if you can back it up middleweight. Doesn't matter if its December or April or August next year - the outcome will be the same, I will obliterate you.
"I'm a seven-foot 20 stone behemoth and I will destroy you middleweight. Find your balls, come see me."
Usyk, who is unbeaten in his 20 professional bouts, currently holds the WBA, IBF, WBO and IBO heavyweight titles.
Fury, on the other hand, appeared to be heading for retirement after knocking out Dillian Whyte at Wembley Stadium in April. The 34-year-old is unbeaten having won 32 of his 33 professional bouts.
A fight between Usyk and Fury could crown the first undisputed heavyweight champion since Lennox Lewis.