Fury claimed Wilder's WBC heavyweight title with a one-sided seventh-round TKO victory in February.
The trilogy was initially scheduled to be completed on July 18 in Las Vegas but with boxing currently suspended in the UK, alongside a diminished ability to train, Arum believes a postponement is now the only choice.
Many believe Fury was unfortunate not to be announced victorious in their first bout - where the result was a draw - with a focus since turning largely towards an undisputed showdown between the Gypsy King and Anthony Joshua.
The highly anticipated match up now looks unlikely to take place in 2020, however, Arum touting October as a potential rescheduled date, Joshuas mandatory defence against Kubrat Pulev also likely to be pushed back.
Speaking to ESPN, Arum emphatically dismissed the chances of a July bout. He said: "Clearly not. 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."
Fury has revealed he is taking the Government's isolation measures seriously and urged his fans to stay indoors.
A post shared by Tyson Fury (@gypsyking101) on Mar 23, 2020 at 2:16pm PDT
In an Instagram video, Fury said: "I would just like to say that I hope everybody is keeping well and staying safe and staying indoors and not going out because of the virus.
“After listening to what the prime minister said, I've taken it deadly seriously, as should you.
“Let's fight this virus together as a nation, as a family and as a team, and do the best to help others not get the virus.
“Stay indoors, it's very, very important, listen to Boris and stay indoors.”