The 22-year-old, who will regain her status as British number one when rankings update on Monday, has been struggling with the issue that first flared up before the French Open.
The former US Open champion was due to compete in the WTA 500 event starting Wednesday, having been offered a wildcard for the prestigious tournament.
Her withdrawal comes as a precautionary measure to rest her back ahead of Wimbledon, which begins on June 30.
