Azarenka, who came into the match a perfect 10-0 in Grand Slam play this year, was upended by Slovakia's Dominika Cibulkova 6-2, 7-6 (7-4).
The 15th-seeded Cibulkova, who advanced to the quarterfinals at Roland Garros for the first time since 2009, raised her career record to 3-6 against top-ranked players with the victory.
She now goes on to face 2010 runner-up Samantha Stosur, who beat American Sloane Stephens 7-5, 6-4 Sunday.
Tenth-seeded Germa Kerber bested Croatia's Petra Martic 6-3, 7-5 to earn a spot in the quarters, while her next opponent, Italian Sara Errani, took out 2009 champion Svetlana Kuznetsova 6-0, 7-5 to advance.
Celebrity Families of 2014 [PHOTOS]