The bout was originally scheduled for July 24.
The change has been enforced, after Fury tested positive for COVID-19.
The British boxer has received his first vaccination dose, but is yet to receive the second.
The new date for the showdown was confirmed by Fury and Top Rank.
“WBC and lineal heavyweight champion Tyson Fury and Deontay Wilder will now conclude their epic trilogy on October 9 at T-Mobile Arena in Las Vegas after the July 24 was postponed due to Fury’s positive Covid-19 diagnosis.
“Tickets purchased for July 24 will be honoured for the rescheduled date,” a statement from the Gypsy King’s Twitter account read.
Fury battered Wilder when they last met in Las Vegas in February 2020.