Cibulkova's exit leaves Sabina Lisicki as the highest seed remaining in the event at No. 5.
Kateryna Bondarnko defeated Cibulkova 6-3, 6-1 and will meet Lisicki in the quarterfinals. Lisicki advanced with a win Tuesday over Alberta Brianti.
Oudin fell to Kerber 6-3, 6-2, with Kerber advancing to meet Johanna Larsson.
Larsson eliminated the sixth-seeded Shahar Peer in their match Tuesday.
Other winners Wednesday were Aravane Rezai and Anastasija Sevastova.
Rezai outlasted Sorana Cirstea and will next take on Elena Baltacha. Sevastova won over Sofia Arvidsson 7-6 (7-4), 6-4 and in the quarterfinals will face No. 8 seed Irina-Camelia Begu.