They won their second-round matches on Saturday to set up the first-time meeting.
"[It's] a match that I look forward to," Barty said about Monday's meeting with Swiatek. "I've hit with her once in Melbourne a few months ago. She's got a seriously impressive game. It's a challenge that we go into with a really clean slate, a little bit of a period of trying to figure each other out, and how our games match up."
Barty won the French Open in 2019, and Swiatek won last year in Barty's absence.
The top-ranked Barty needed three sets to beat 80th-ranked Tamara Zidansek. Barty struggled with her first serve, but she compensated by striking nine aces and saved nine break points to outlast Zidansek 6-4, 1-6, 6-3. That took her win streak on clay to 13 matches after she claimed the Stuttgart title last week.
"A really tough match," Barty said. "[I] made a lot of errors. I think I was missing in the right way, but still just a foot or two here or there makes a big difference. I felt like there were probably too many loose ones for me today."
Swiatek brushed aside Laura Siegemund 6-3, 6-3, the Polish player's ninth win in a row on clay.
Kerber broke Kvitova's serve to start both sets. But Kvitova canceled the advantage right back and then broke Kerber's serve to close it out.
"I don't think that I really played, like, bad games when she broke my serve," Kvitova said. "It was kind of important to stay calm, which I did very well, I think, through the whole match. I just took her straight away back."