Venus Williams upset Kiki Bertens as five seeds fell at the Western & Southern Open.
A left forearm injury has troubled Petra Kvitova for some time and will force the Czech to miss next week's Rogers Cup in Toronto.
Serena Williams turned on the style at Wimbledon on Saturday but knows there are major threats to her title chances in the women's draw.
Serena Williams still has plans for the weekend at Wimbledon after winning on Thursday, but Angelique Kerber is heading home early.
Petra Kvitova has confirmed she intends to play Wimbledon after suffering no ill-effects from practising at the All England Club.
Two-time Wimbledon champion Petra Kvitova's participation in this year's event is in doubt after she withdrew from the Birmingham Classic.
With Karolina Pliskova, Kiki Bertens, Petra Kvitova and Angelique Kerber out of the French Open, Naomi Osaka will remain world number one.
Diane Parry put Amelie Mauresmo's lesson into practice, while Kiki Bertens and Serena Williams were round one winners at the French Open.
Having played through the pain in recent weeks, an arm injury will keep Petra Kvitova out of the French Open.
While Simona Halep insisted fitness was not an issue ahead of the French Open, Naomi Osaka eased through at the Internazionale d'Italia.