Williams’ defeat means her quest to equal Margaret Court’s record of 24 grand slams continues.
The American, who lost 6-3 7-5 to Rybakina, hasn’t made it past the fourth round on the 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 starts on June 28.
“I’m kind of excited to switch surfaces, but historically I have done pretty well on grass,” said Williams, who is a seven-time Wimbledon singles champion.
“I have done pretty well on clay too. Just not this particular season.”
Her victory over Williams ensured the 21-year-old Rybakina advanced to her first grand slam quarterfinal.
“I am so happy with my match, it was amazing,” said Rybakina, who will now play Anastasia Pavlyuchenkova for a semifinal spot.
“I was small, of course I was watching her matches on TV,” added Rybakina of Williams.
When Williams won her first grand slam title at the US Open in 1999, Rybakina was just two months old.
“It’s difficult to expect anything, because you watch on TV and that’s completely different when you come on court and you feel the power and everything,” said the world No. 22.
“I knew that the serve was going to be difficult for me to return. She’s powerful, but I was ready. Then after few points I felt it comfortable, so nothing.”
Federer is targeting a ninth Wimbledon title on his favorite grass court surface later this month.