The British heavyweights are due to fight each other later this year but the promoter explained that Joshua must come through his July fight against Kristian Prenga unscathed to make the long-awaited clash a reality.
Hearn told Sky Sports: "In my opinion if either fighter loses, you cannot do the fight.
"I will feel sick at the ringwalk on July 25. Especially with what AJ's come back from. I mean there is that worry. Will he be the same? Everything we see in camp and in sparring lends us to suggest yes. But there's a lot to overcome. That's the importance of this fight as well in July."
The Matchroom boss added: "Now we have signed to fight Tyson Fury. He has signed to fight Anthony Joshua. The only thing that stands in the way is July 25."
Fury is believed to be looking for a tune-up bout of his own and Hearn is hoping to The Gypsy King on the same bill as Joshua's clash with Prenga in Saudi Arabia's capital Riyadh.
He said: "We don't have a problem with that. That's down to Turki [Alalshikh] to see where he wants to land. It might be difficult for Fury to go underneath Joshua on that card (but) I don't know.
"I don't think he [Fury] is going to be having a fight of any significance, even not the likes of (Arslanbek) Makhmudov. I don't even think they'd have a fight at that level. They've got to do what they've got to do. They've just had 12 good rounds and we look forward to hopefully less rounds than that but going through the gears and warming up for the big one.
"I think everybody's extremely focused, now that both fighters have signed, on just getting through the next couple of months and making sure we can give the world this mega-event."