Dementieva next meets fifth-seeded Caroline Wozniacki, who routed Virginie Razzano 6-2, 6-0.
Sabine Lisicki, who is seeded 16th and ousted Venus Williams on Thursday, beat Elena Vesnina 6-4, 6-0. Marion Bartoli, seeded sixth, was to play Melinda Czink.
Dementieva won the first set 6-4, and was up 1-0 in the second against Cibulkova in a match featuring long baseline rallies. Cibulkova, seeded seventh, played with her left thigh wrapped and had it rewrapped between sets before retiring. She waved to the crowd as she walked off the green clay.
Cibulkova led 4-3 in the first set before Dementieva won three consecutive games, surrendering only three points. She is 3-1 against Cibulkova.
"She came with the tape on her leg and I didn't know if it was bad or not, so I just feel sorry she couldn't finish the match," Dementieva said.
Wozniacki won last week on clay at Ponte Vedra Beach, Fla.
MONTE CARLO MASTERS: In Monaco, top-ranked Rafael Nadal moved one step closer to his fifth consecutive final in this event, defeating Ivan Ljubicic 6-3, 6-3 in his second match of the day.
Nadal also improved his winning streak in Monaco to 25 matches.
Nadal will face fourth-seeded Andy Murray, who reached his first career semifinal on clay after beating Nikolay Davydenko 7-6 (1), 6-4.
Third-seeded Novak Djokovic also reached the semifinals, defeating No. 7 Fernando Verdasco 6-2, 4-6, 6-3. Djokovic will meet No. 13 Stanislas Wawrinka.