Williams’ defeat means her quest to equal Margaret Court’s record of 24 Grand Slam tournaments continues.
The American, who lost 6-3 7-5 to Rybakina, hasn’t made it past the fourth round on clay at Roland Garros since 2016.
She will now turn her attention to Wimbledon – the third grand slam of the season – which is played on grass and begins on June 28.
“I’m pretty excited to change surfaces, but historically I’ve done pretty well on grass,” said Williams, a seven-time Wimbledon singles champion.
“I have done really well on clay as well. But not this season in particular.”
His victory over Williams saw Rybakina, 21, advance to his first Grand Slam quarter-final.
“I’m so happy with my game, it was amazing,” said Rybakina, who will now face Anastasia Pavlyuchenkova for a place in the semi-finals.
“I was little, of course I watched her games on TV,” added Williams’ Rybakina.
When Williams won his first Grand Slam title at the US Open in 1999, Rybakina was just two months old.
“It’s hard to wait for anything, because you’re watching TV and it’s a whole different thing when you come out on the court and feel the power and everything,” said the world number 22.
“I knew the serve was going to be hard for me to return. She’s powerful, but I was ready. Then after a few points I felt comfortable, so nothing.”
Federer is aiming for a ninth Wimbledon title on his favorite turf later this month.
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