Bjorn, who has played just one of the past six US Opens, will be replaced by amateur Andrew Dorn at the major.
Dorn takes his place in the field as the first alternate at the US Open sectional qualifier held in Ohio on Monday.
Bjorn, a 15-time winner on the European Tour, appeared in good form at last month’s BMW PGA Championship at Wentworth.
The 43-year-old equalled a course record after holing eight birdies and an eagle to card an opening round 10-under-par 62, though he eventually faded as Rory McIlroy triumphed.
Meanwhile, South African Richard Sterne has also withdrawn after failing to overcome an injury.
American Scott Langley, who made the cut at the 2010 US Open as an amateur, is Sterne’s replacement.
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