Kvitova recorded a 6-2, 6-0 victory over eighth-seeded Johanna Larsson of Sweden in her quarterfinal match. Kvitova won 11 consecutive games during the match and next faces American Lauren Davis in the semifinals.
"After the match yesterday I felt really ill and really sick," Wozniacki told reporters on Thursday. "I did everything I could to feel better today but unfortunately I'm not strong enough or feeling good to play today. I need to think about my health.
"Of course, I'm disappointed because I love to play here and of course was trying to win the tournament, but health comes first."
Niculescu will face third-seeded Kiki Bertens, who rolled to a 6-0, 6-4 victory over Denisa Allertova of the Czech Republic.
Bertens needed just 54 minutes to wrap up the victory.
"Everyone is really tired at the end of the year, and so am I, so it's really good to have short matches like this to get ready for the semifinals," Bertens said. "I'm just going to play here, have fun, and see how it goes."
Davis advanced by posting a 2-6, 7-5, 6-2 victory over Germany's Andrea Petkovic.