The 21-year-old Japanese was scheduled to face sixth seed Kiki Bertens after coming through two matches on Thursday in the rain-affected tournament but said she was forced to withdraw due to pain and swelling at the base of her thumb.
The injury could be a concern for Osaka, who has won the last two grand slams, ahead of the French Open at Roland Garros with the first games due to start on 27 May.
Osaka also had to pull out of the Stuttgart Open because of an abdominal problem.
She follows Serena Williams out of the tournament, with the American withdrawing due to a knee issue. Caroline Wozniacki also pulled out ahead of her first-round match due to a calf complaint.
"I woke up this morning and couldn't really move my thumb," Osaka told reporters. "I tried to practise and grip my racket but I couldn't, and I kept feeling this pain when I tried to move my hand in different directions.
"Right now I'm... in between sad and disappointed because I really wanted to play my match today. For me, it was sort of a test to play against Kiki because she's playing really well and I wanted to see how well I could do today.
"I didn't feel anything yesterday. That's why I'm kind of confused right now because I literally woke up in the morning and couldn't move my thumb. So I was like, maybe I slept on it and maybe it will go away, but it didn't."
Additional reporting from Reuters