The Greek tennis star says he is a huge fan of the Australian actor and would love her to support him from the Melbourne Park stands.
His surprise shout-out to Robbie came after Tsitsipas scored a 6-3 7-6 (7-2) 6-4 win against unseeded Czech Jiri Lehecka in the quarter-finals on Tuesday.
Tsitsipas was partway through explaining his impressive display to on-court interviewer Jim Courier, detailing how it took "experience and some good Spartan attitude" to get the better of Lehecka, when he mentioned the 32-year-old Hollywood star.
Robbie, married to English film producer Tom Ackerley, became well known in Australia and the UK for her role in the soap opera Neighbours before turning to Hollywood.
Her career includes prominent roles in movies including The Wolf of Wall Street, Suicide Squad and I, Tonya, as well as being the voice of Flopsy Rabbit in the Peter Rabbit film series.
"Can you hear them? Australia is such a great country," Tsitsipas said, reacting to roars from the crowd.
"I like a lot of great Aussie things. One of my favourite actresses comes from Australia, Margot Robbie."
Former Australian Open champion Courier, surprised by that unprompted mention, said: "Are you pitching right now?"
That prompted Tsitsipas to say: "It would be nice to see her over there one day."
Was that an invitation to Robbie?
"Absolutely," Tsitsipas said.
The 24-year-old Greek player soon stressed that his Robbie fandom was not the main reason for him enjoying Australia.
"That's not it," Tsitsipas said. "The people are very welcoming. I've said that so many times and will keep saying it because it's true.
"I grew up in a place that's very similar in terms of conditions and lifestyle and find myself feeling home when I'm here because it's not too tropical, and it's not too humid, and it very much feels like home.
"The French players have Roland Garros as their home grand slam, the British players have Wimbledon, the Americans have the US Open; for me, the Australian Open is always going to be my home grand slam.
"I would love one day hopefully winning the Aussie Open and giving a bit portion of the prize-money to build a school in Victoria which is the state of education. I'd like to do that."