Rybarikova, seeking the fourth title of her career, ousted Flipkens 7-6 (13-11), 5-7, 6-3.
That set up a meeting with third-seeded Sabine Lisicki, who eliminated Kristina Mladenovic 6-3, 6-3. Lisicki is the only seeded player left in the event.
The other semifinal will send Stefanie Voegele against Marina Erakovic.
Voegele breezed by No. 4 seed Heather Watson 6-1, 6-2 and Erakovic downed Jamie Hampton 7-5, 6-2. Erakovic defeated second-seeded Sofia Arvidsson in the second round.
Celebrity Families of 2014 [PHOTOS]