Wozniacki -- the No. 13 player in the world -- fell in three sets to the No. 68 Kudermetova. The Russian beat the Dane 0-6, 6-3, 6-3 in the round of 128 matchup at Roland Garros.
Kudermetova battles Zarina Diyas in the round of 64 on Wednesday in Paris. Wozniacki lost to Daria Kasatkina in the fourth round of the 2018 French Open. She advanced to the quarterfinals in 2017, but has never won the grand slam. She was champion of the 2018 Australian Open.
Kvitova announced her withdrawal Monday on Twitter, citing a forearm injury.
"I'm so disappointed to have to announce my withdrawal from Roland Garros," Kvitova wrote. "I've had pain in my left forearm for a few weeks and last night an MRI confirmed a grade two tear, which unfortunately could get a lot worse if I play today."
"Two years ago, I made my comeback here at Roland Garros, so I'm truly sad not to be able to play here this year. It is a really tough decision to make, but I wish the tournament all the best for a successful event and can't wait to be back in 2020."
The women's final at the 2019 French Open is set for June 8 at Roland Garros. The men's final is on June 9 in Paris.