World record holder Robles had been scheduled to face China's Liu Xiang and American David Oliver in Eugene, Oregon in a showdown of the three fastest 110 metres hurdlers of all-time.
When Robles did not receive his visa until Thursday, however, his coach decided that did not give him enough time to fly, rest and be prepared to take on a field also including world outdoor and indoor champions, Americans Jason Richardson and Aries Merritt.
"It is very disappointing," meeting organiser Tom Jordan said. "We hope to have him and other Cuban athletes here in the future."
Cuban officials confirmed Robles would still compete in the New York Grand Prix, his first ever race in the United States.