The world number six was able to play her first match in the White group on Tuesday but was toppled 6-3 6-2 by Poland's Agnieszka Radwanska in a contest that saw the Czech commit a whopping 41 unforced errors.
Australian Stosur will complete the other matches Kvitova was due to play in the four-woman round robin group against Russia's Maria Sharapova and Italy's Sara Errani.
The WTA Championships features the world's top eight women with the Red group comprising Victoria Azarenka of Belarus, American Serena Williams, Angelique Kerber of Germany and Li Na of China.
Kvitova will lead the Czech Republic in their Fed Cup title defence against Serbia next month in Prague, however.
The Czechs will seek to become the third consecutive nation to retain the title after Italy in 2009-10 and Russia in 2007-2008.
World number six Kvitova helped her country defeat Italy in the semi-finals.
"She is a top player and, regardless of the WTA championships, I'm convinced she is preparing well for the Fed Cup weekend," team manager Petr Pala said.
Lucie Safarova, Andrea Hlavackova and Lucie Hradecka will complete the team who face Serbia from November 3-4.
The Czech men's team will take on Spain from November 16-18 in the Davis Cup final.
A win by both Czech teams would mark the first time since 1990 that a nation has captured the men's and women's titles in the same year.