Following up her big win over Maria Sharapova in the previous round, Bouchard led Kerber 6-3 5-0 before the world number two withdrew due to a thigh injury.
Kerber had broken her opponent in the opening game of the match but soon appeared to be ailing as the Canadian took full control.
Halep outlasts determined Mladenovic to retain Madrid title
Bouchard responded by breaking Kerber four times to take the first set, and continued her dominance in the second with her opponent clearly wilting.
Bouchard will face Svetlana Kuznetsova in the last eight after the Russian eighth seed beat Qiang Wang of China 6-4 7-5.
Third seed Simona Halep also reached the quarter-finals after coming through a tough 6-4 4-6 6-4 win over Sam Stosur.
The Romanian will next play American Coco Vanderweghe who needed nearly two and a half hours to see off Spain's Carla Suarez Navarro 5-7 6-4 7-5.
Kristina Mladenovic will play Sorana Cirstea in the last eight after wins over Oceane Dodin and Misaki Doi respectively.
Kiki Bertens and Anastasija Sevastova complete the quarter-final line-up after wins over Irina-Camelia Begu and Lara Arruabarrena.
Bouchard reveals inspiration behind grudge-match victory over Sharapova
Bouchard wins Sharapova grudge match after 'cheater' claim