Wozniacki, 28, had retired due to injury from her two previous matches before the French Open but she appeared to have rediscovered her form as she swept through the first set on centre court.
But the 13th seed could not maintain the standard. "I think she got very lucky at the start of the second set and took advantage of the opportunities she got," said Wozniacki.
"I ran out of steam in the end and made some unforced errors that I don't usually do, so that was very frustrating. She had a few net chords and good shots on some of the important points at the start of the second set.
"It's definitely frustrating. You want to win, you work hard and you want to see results. It hasn't been a great year for me so far, so I'm going to work hard and try and turn it around."
Kudermetova, 22, who had never played before in the main draw at the French Open, said: "I was a little bit nervous at the start of the match but I took it game by game and tried to be more aggressive."