Williams’ failure meant her search to match the 24 Margaret Court statistics on the crash.
The American, who defeated Rybakina 6-3, 7-5, has not made it to the quarterfinals at Roland Garros since 2016.
She will now turn her attention to Wimbledon – the third major prize of the season – which is played on the grass and starts on June 28.
“I was excited to change the cliff, but historically I have done well on the grass,” said Williams, a seven-time Wimbledon champion.
“I do really well in clay as well. Not just this season.”
Her victory over Williams put 21-year-old Rybakina through to her first semifinals.
“I’m very happy with my match, it was amazing,” said Rybakina, who will play Anastasia Pavlyuchenkova for the final.
“I’m young, of course I watched her match on TV,” said Williams’ Rybakina.
When Williams won the first US Open in 1999, Rybakina was just two months old.
“It’s hard to expect anything, because you watch TV and it’s completely different when you go to court and you feel power and everything,” said the world number 22.
“I know service will be difficult for me to return to. She has power, but I’m ready. After a few points I feel comfortable, so nothing.”
Federer is aiming for his ninth Wimbledon title on his favorite pitch later this month.