The decision to pull out of the event was a precautionary measure and Bolt's agent Ricky Simms expects the sprinter will resume his race schedule after a two-to-three week layoff.
"At the moment there is no change to the rest of his programme," Simms said in a telephonic interview from Munich, where Bolt has been undergoing treatment.
Bolt, who has inflammation in the left Achilles tendon, is not scheduled to run again until a 200 metres in Lausanne on July 8, Simms said.
He was scheduled to face American Tyson Gay in New York in a 100 metres showdown between the world's two fastest men.
"I developed a stiffness in my Achilles tendon last week and sought medical attention," Bolt said in a statement released by the New York meeting's organisers.
"After careful consultation with Dr. Hans Müller-Wohlfahrt at his clinic in Munich, I have been advised to take a two-three week break as a precautionary measure to avoid risking further damage," he added.
The withdrawal is another setback for the new Diamond League global circuit, which already had lost world record holders Yelena Isinbayeva and Kenenisa Bekele for the season.
Russian pole vaulter Isinbayeva is taking a break after failing to medal at the world indoor championships.
Ethiopian Olympic and world 5,000 and 10,000 metres champion Bekele is sidelined with a ruptured calf muscle.
Bolt had run once on the circuit, winning 200 metres in Shanghai. He is expected to compete five more times on the Diamond League this season.
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