The second-seeded Kvitova, a three-time champion in Madrid, is coming off a title in Stuttgart and is the only woman to win two tournaments this season.
Kvitova is the most successful women's player in Madrid with 27 wins and only six losses. Her other titles in the Spanish capital came in 2011 and 2015.
Seventh-seeded Kiki Bertens opened with a 6-3, 6-2 win over Katerina Siniakova, while eighth-seeded Andrea Petkovic lost to Polana Hercog 4-6, 7-6 (1), 6-1.
Top-seeded Naomi Osaka makes her debut on Sunday against Dominika Cibulkova.