Joshua watched as his fellow world champion destroyed Dominic Breazeale in just two minutes on Saturday night.
Wilder knocked out his mandatory challenger in the first round, three years after Joshua took seven to do the same.
Wilder then insisted he will fight Joshua but Hearn has demanded it happen in 2019.
The Brit must first overcome Andy Ruiz Jr in New York on June 1.
"That was an impressive win for Deontay – he's exciting to watch," Hearn told sky Sports.
"He has taken care of business, now AJ needs to do the same against Ruiz Jr at Madison Square Garden on June 1.
"The fight with AJ and Wilder is the biggest fight in the sport and all being well in two weeks' time it must happen next – no excuses, this is the fight that will change the sport globally.
“It's a legacy fight and AJ wants it so bad. Two big, fast, dangerous and fearless world heavyweight world champions that can turn the lights out with a blink of the eye – it's a must.
"First things first, taking care of business on his American debut on June 1 and send a message straight back."
After knocking out Breazeale, Wilder said: I've got a lot of obligations to fulfil," said Wilder. "But if that date is open for me, you may see Deontay Wilder there [on June 1].
"When it's a good scrap, a good fight that people want to see, you might find me there.
"I can't say right now, I can't promise you that but when that time comes we'll see what happens."