Raonic, from Thornhill, Ont., had a bye into the second round. He was eliminated by Ricardas Berankis of Lithuania 6-3, 4-6, 6-3.
Not long after, an out-of-sorts Cibulkova was eliminated by tenacious Vitalia Diatchenko of Russia 4-6, 6-2, 6-2.
Raonic's loss put him in danger of failing to qualify for the ATP Finals in London next month. He blamed the defeat on illness.
"I was sick for the last 10 days, so I was in bed the whole time, and I only was able to prepare the last two days," he said.
Raonic, who holds the eighth and last qualifying place for the tour finals, said "there's not really that much of a heartbreak" in exiting Moscow so early, since more points were on offer in the Paris Masters this month.
Playing with his right arm in strapping, the ninth-ranked Raonic struggled with his usually powerful and accurate serve, landing only 59 per cent of first serves.
For the 116th-ranked Berankis, it was his first career win against a top-10 player. His reward is a quarterfinal against fifth-seeded Roberto Bautista Agut of Spain.
Cibulkova won the first set against local qualifier Diatchenko, but the Czech then suffered serious problems with her serve as the Russian broke her nine times in front of an overjoyed home crowd.
"She played aggressive," Cibulkova said of Diatchenko. "I made a few mistakes and she stayed aggressive throughout the whole match and just put me under pressure."
Just three seeded players reached the women's quarterfinals, led by No. 4 Lucie Safarova.
Diatchenko, ranked 140th, returned to playing only this year after two years sidelined with knee injuries. Her win over Cibulkova will bring the Sochi native closer to her highest ranking before her injury, 105th.
In the last eight, Diatchenko faces fifth-seeded fellow countrywoman Anastasia Pavlyuchenkova, who beat Alison Riske of the United States 6-2, 6-2.
In other results from the men's draw, third-seeded Ernests Gulbis of Latvia booked a quarterfinal with Andreas Seppi of Italy, and last year's runner-up, Mikhail Kukushkin, knocked out fourth-seeded Fabio Fognini of Italy 6-4, 6-2.
Kukushkin next plays 2009 champ Mikhail Youzhny, who put out Juan Monaco of Argentina 6-3, 7-6 (6).
U.S. Open champion Marin Cilic, seeded second, faces sixth-seeded Tommy Robredo.Suggest a correction