The announcement comes less than 10 days before the start of the French Open, the year's second Grand Slam, which starts May 26.
Sharapova says on Twitter that she "didn't recover after being sick last week and it got me again last night."
Sharapova showed no problems as she beat 16th-seeded Sloane Stephens 6-2, 6-1 Thursday, and she was runner-up to Serena Williams in last week's Madrid Open.
The withdrawal means Errani advances to the semifinals. Her opponent will be either third-seeded Victoria Azarenka or ninth-seeded Sam Stosur.
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