Dominika Cibulkova of Slovakia (Photo; AP)
Cibulkova, seeded 15th, will play either Samantha Stosur of Australia or Sloane Stephens of the United States for a place in the semi-finals.
Azarenka won the Australian Open in January and had been expected to coast past Cibulkova having beaten her seven times out of eight previously.
But the little Slovakian, who reached the semi-finals here in 2009, handled the cold, windy conditions on the Suzanne Lenglen court far better than the tall Belarusian.
"It wasn't satisfying at all, not satisfying being out there playing like that. I do not know what to find positive in that. No excuses, just a bad performance," Azarenka said
The top seed looked formidable when she broke her opponent in the opening game but Cibulkova immediately equalised and then proceeded to break the favourite two more times in the set and six times in the entire match.
In the second set, Azarenka appeared to be getting back on track as she broke to lead 2-0 but 23-year-old Cibulkova dug deep to run off four games in a row.
In the fifth game, Azarenka flew into a rage after she flicked a drop shot into the next, getting a warning for smashing her racquet on the clay as the crowd jeered.
But the 22-year-old composed herself to level at 4-4 and was up 0-30 in the crucial ninth game, only to see Cibulkova hold her serve courtesy of a backhand error by the world number one.
Azarenka recovered to 5-5 and took the next game with a hard and flat backhand return.
But Azarenka was broken again when a forehand went wide, sending the match into a tiebreaker.
Cibulkoba raced to 6-4 and clinched the match with a sharp backhand winner that she set up with a sneaky drop shot, leaving Azarenka stranded at the net as her French Open dreams came to an end.
(For more sports news and updates, follow Ahram Online Sports on Twitter: @AO Sports)