Fury, 32, looked set to finalise a fight for all four world titles against Anthony Joshua in Saudi Arabia.
But the all-British affair fell through when Wilder's team won an arbitration hearing stating the American had a right to a third fight with Fury.
Fury attended Josh Taylor's win over Jose Ramirez in Las Vegas on Saturday, where he signed his fight contract.
"He's getting seriously smashed to bits," Fury said. "I'll give him another shoulder injury, another bicep injury, another leg injury.
