Tyson Fury maintained his unbeaten professional boxing record with a convincing win over Schwarz in Las Vegas on Saturday night.
He outclassed the German and stopped him with just seconds of the second round remaining.
Fury is now eyeing up a rematch with WBC world heavyweight champion Deontay Wilder after the pair drew in December.
Anthony Joshua did hold the other three belts before surprisingly being beaten by Andy Ruiz earlier this month.
A rematch to give Joshua the opportunity to earn his straps back is expected to happen.
But with rumours that AJ quit against Ruiz, Fury has sent a message to Schwarz over his bravery.
Fury posted on his Instagram story: “I want to send my respect to Tom Schwarz who came to fight, came to win.
“Got hit with a shot that hurt him but he still tried to press, still fired back.
“He believed in himself. He was not happy to just take part and was heartbroken to lose the fight and I respect that.
“Losing to the number 1 in the world is no shame.
“A young hungry lion you will come again Tom.”
The latest apparent dig at Joshua comes after Fury had mentioned the 2012 Olympic gold medalist during his press conference.
When asked if his victory over Schwarz was more satisfying given Joshua’s shock, Fury said: “We saw a British fighter [Joshua] travel over to America a week ago or the week before. He looked like he didn’t want to be in there.
“For whatever reason, we’re not going to go into that tonight, it’s not my concern or business.
“But tonight was Tyson Fury Las Vegas. It doesn’t get any bigger than this. This is the biggest thing that has happened in my career, topping the bill at MGM Grand.
“In the car on the way in with my wife I said, ‘I think we’ve made it Paris.’ She said, ‘Why?’ And I said, ‘Because we’re headlining in Vegas. This is it.’
“And we got a good show and I was happy with how everything went. All my family and all my friends and everybody who came over were all happy with the performance.”
The future of heavyweight boxing appears to be dependant on what Fury, Wilder and Joshua do.
Wilder is expected to fight Luis Ortiz in the autumn with a rematch with Fury expected early in 2020.
Fury is also likely to have another fight before the end of the year.
For Joshua, the rematch with Ruiz is likely to be next.
Lose that, and many believes AJ’s career is all but over. Win, and he puts himself back in the mix for a battle with the other two.
Negotiations had been long and ongoing for an undisputed clash between Joshua and Wilder before the Brit was beaten in New York.
Now, it appears Fury vs Wilder 2 is the main event.