Barty had strapping on her left thigh and struggled with her movement throughout the first set, which she lost 6-1.
The 25-year-old had a medical time out but never recovered and, with the match even at 2-2 in the second set, decided to call it quits.
It means Linette will be in the next round by default, with the Pole looking to win the tournament for the very first time.
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