Kvitova said she had a sore throat and stomach problems. She was scheduled to see a doctor later Wednesday.
The Czech player lost her opening match Tuesday, falling 6-3, 6-2 to Agnieszka Radwanska.
The season-ending tournament brings together the top eight players in the world. Stosur was the first alternate.
Kvitova said she was hoping to recover in time to play in the Fed Cup final against Serbia next week.
"I try my best to be ready for the Fed Cup. It's final at home and I really want to play in front of our crowd, my family and friends, and try to win the Fed Cup title again," Kvitova said. "I will try my best to be ready for the weekend."