In a brief post on Twitter, the WBC confirmed the July 24 bout had been postponed but did not say when the trilogy fight would be rescheduled.
“Fury vs Wilder III will be postponed,” the WBC said. “We wish Tyson Fury’s team and him speedy recovery from COVID.”
Multiple reports in the US and Britain have said Fury and several members of his team had tested positive for Covid-19 at their Las Vegas training base.
ESPN reported that the fight at Las Vegas’s T-Mobile Arena had been tentatively rescheduled for October 9.
The positive test was the latest twist to what has been a tortuous year for Fury.
The undefeated “Gypsy King” had been set to face a money-spinning heavyweight unification fight against fellow Briton Anthony Joshua.
However that fight was scuppered after an arbitrator ruled that Fury was legally obligated to face Wilder in a third fight.
Fury handed Wilder a brutal beating in seven one-sided rounds in their second fight in February 2020.
Their first fight, in December 2018, ended in a controversial split-decision draw in which Fury was knocked down twice.
Neither Wilder, 35, nor Fury, has fought since their bout in Las Vegas last year.