The second seed looked to be heading for a routine win when she took the opening set against Ukraine's Yuliia Starodubtseva in the second round on a sweltering Court Suzanne Lenglen on Wednesday.
But Rybakina began to find life a lot more difficult and Starodubtseva, ranked 55 and in good form, won nine of the next 10 games to lead 3-0 in the decider.
The Kazakh player's errors were far outpacing her winners as she toiled in the heat and, although she recovered to force a tie-break, Starodubtseva completed the biggest win of her career with a 3-6 6-1 7-6 (10-4) success.
It is Rybakina's earliest grand slam exit since a second-round loss at the US Open in 2024, with an eventual tally of 71 unforced errors telling its own story.
"It's just a pity because I think I was practising well before the French Open, and I was feeling also good in the practices and thought that I can raise the level," said the former Wimbledon champion.
"But actually today it was a very bad performance, too many unforced errors, and I didn't feel the greatest. So I was trying to find a way, but it clearly didn't work."
Iga Swiatek has continued her bid to rediscover her best form at the French Open, reaching the third round with a 6-2 6-3 victory over Czech Sara Bejlek in a match littered with unforced errors.
The four-times champion, who has lost only twice at Roland Garros since 2020, had far too much quality for her opponent but made 38 unforced errors, including a series of double faults.
Swiatek, the world No.3, explained her lack of precision by the nature of the opposition.
"She was pretty good in defence, and I had many opportunities to attack. Sometimes even too many. So when you attack, you're going to make more mistakes, because it's easier to push the ball back than to actually add a lot of energy to it and try to open the court," the 24-year-old said.
"So, yes, sometimes I made some mistakes while playing these high balls, because the ball is jumping quite high. It's not easy to judge if it's the one that you should go or stay back and wait for the next one.
"The rhythm wasn't quite obvious. But I didn't mind. I wanted to be flexible and adjust and play my game. I had some moments where the mistakes happened, but at the end I feel like I was the one who had control over the game, and it was up to me if I'm going to finish these points or make a mistake."
Swiatek will now face fellow Pole Magda Linette, who overcame 2017 French Open champion Jelena Ostapenko, for a place in the last 16.
Elina Svitolina extended a run of solid form with a 6-0 6-4 victory over Kaitlin Quevedo. Svitolina is on an eight-match winning streak after lifting the Italian Open trophy.
Switzerland's Belinda Bencic, the 11th seed, beat American opponent Caty McNally 6-4 6-0.
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