Cuban Robles suffered a slight swelling in his left leg during training and the 110 metres hurdles world record holder would need a week of specialised medical treatment, his coach Santiago Antunez said.
"It will not rule out his attendance at the London Olympics and he will compete again in late June in Europe," Antunez said.
The Cuban athletics federation said Robles's injury was not serious, but experts had recommended he focus on treatment rather than competing.
Robles's countryman Orlando Ortega will compete in New York, however. The 20-year-old defeated Robles earlier in the season in Cuba.
Robles had been scheduled to face the United States' top hurdlers in New York a week after he withdrew from the Diamond League meeting in Eugene, Oregon, because of a delayed visa.
The trip would have been the 25-year-old's first competition in the U.S., and his race in Oregon had been billed as an Olympic preview featuring former world record holder Liu Xiang of China, the second fastest 110m hurdler behind Robles.
Liu lived up to the billing by matching Robles's world record of 12.87 seconds, but was denied a share of the mark because of an assisting wind.
The world's fastest two hurdlers are now unlikely to meet before the Olympics. Liu does not plan to race again until the London grand prix in July.
The pair have not met outdoors since Robles, the race winner at last year's world championships, was disqualified for interfering with Liu, who was awarded the silver medal.
Liu has won six of nine career races between the two outdoors, but other than the world championship race, they have not met outdoors since 2007, primarily because of injuries to Robles.
The Cuban has been slightly more successful indoors, winning two of their four races including the 2010 world indoor championship.