The 23-year-old, who became the first Australian woman to reach the top of the WTA rankings for 43 years on Sunday when she won the Birmingham Classic, has aggravated an arm injury.
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"It's an injury I've had to manage since I was 16 years old," Barty told reporters at Devonshire Park on Monday.
"It happens when I have a spike in load, it's just a bone stress injury and I need to look after it."

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Barty, who won the French Open earlier this month and is on a 12-match winning streak, said she was optimistic she would be ready in time for Wimbledon where she will be the top seed and many people's favourite.

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"I think it will be fine but we will have to make sure that we manage it carefully over the next three or four days and that I'm ready to go next week," she said.