Britain's unified champion had wanted to fight Fury at the end of the year, with all the world heavyweight belts at stake, but the new WBC champion is contractually obliged to face Wilder first and the coronavirus has delayed plans for another fight in Las Vegas this summer.
With Nevada casinos shut and travel from Europe to the US suspended in an effort to slow the spread of the virus, Top Rank chairman Arum says there is no way Fury-Wilder 3 can go ahead as scheduled at the MGM Grand.
"Clearly not," Arum, Fury's co-promoter with Frank Warren, told ESPN when asked about the bout being held on July 18.
"We don't even know if the MGM will be open by then.
"You could not guarantee the fighters that the event would take place on that date. We couldn't convince them or ourselves.
"Where were they going to train for it? It just made no sense. You just have to take a step back. How are you going to sell tickets? It's absolutely ridiculous to say the fight is on when the Brits can't even get there."
In their first two fights, a large contingent of vocal British fans packed the arenas to support Fury, known as the 'Gypsy King'.
"So everybody has to take a step back. Boxing is not isolated. It's part of what's happening in the world," Arum said.
"So possibly the fight will be in early October."
Matchroom Boxing boss Eddie Hearn had remained hopeful that he could fit a blockbuster battle with Fury into the schedule for Joshua, who is due to defend his world titles against Kubrat Pulev at Tottenham Hotspur Stadium on June 20, live on Sky Sports Box Office.
Hearn had told Sky Sports last week that Joshua's undisputed battle with Fury could take priority over an IBF mandatory title defence against Pulev.
He said: "Well I think, all of a sudden, does the Joshua-Fury fight start taking priority, maybe over a Pulev fight, if the Pulev fight extends beyond the summer? There's so much that could happen right now.
"I mean anything is possible, but contractually Deontay Wilder is going to want his fight next, whether that's in July or whether there's a force majeure that takes that to October, November wherever."
Dillian Whyte is the mandatory challenger for the WBC belt and the governing body has said he will receive his world title fight by February 2021, which could further delay a Joshua-Fury fight.