Stefanovic then hit back at Morgan during Thursday morning's Today show, saying his comments were "disgraceful."
"I think she is an amazing, amazing woman and I think she's doing her very best at the moment, and she's got a lot on her plate and is doing it so beautifully," Stefanovic said.
"She's such a great export for Great Britain, I mean - what is that guy on?"
Morgan then replied to Stefanovic's comments on Twitter, telling the Channel Nine presenter to "pipe down."
Meghan and Harry are currently in Sydney touring Sydney's iconic Bondi Beach.