Spanish third seed Badosa retired at 6-3 2-1 against Veronika Kudermetova while Sabalenka, seeded seventh, lost 12 of the last 13 games - including eight in a row - against Italy's Camila Giorgi.
Badosa was forced to retire with a right calf injury. The 24-year-old, who reached the quarter-finals last year, was considered one of those in the women's draw who could challenge Swiatek on clay.
Playing on Court Suzanne Lenglen, Badosa required medical attention for a right leg problem during the match and then decided early in the second set that she could no longer continue.
Sabalenka went down to big-hitting Italian Giorgi 4-6 6-1 6-0 on Court Simonne Mathieu.
Sabalenka, a former world No.2, won the hard-fought opening set but then was reduced to a mere spectator as Giorgi scorched the court with winners.
The Belarusian managed to win only one more game as Giorgi completed a remarkable comeback win in an hour and 42 minutes.
The 30-year-old Giorgi will next meet the No.20 seed Daria Kasatkina.
Jessica Pegula, the No.11 seed, powered into the last 16 for the first time with a 6-1 7-6 (7-2) win over last year's semi-finalist Tamara Zidansek.
Reuters
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