The Spaniard has pulled out of the super-bantamweight showdown after his father was taken ill during training camp and has since had to have a leg amputated.
Martinez immediately left camp and then made the decision not go ahead with the fight in Belfast's King's Hall, on September 10, live on Sky Sports HD3.
It leaves Frampton's promoters Matchroom Sport searching for an opponent but they have confirmed the 24-year-old will still feature on a bill being topped by Paul McClosley's WBA light-welterweight eliminator with Breidis Prescott.
"Irish fight fans can be assured that Carl will remain on the bill," said Eddie Hearn.
"He has trained for a big fight and that's exactly what we are going to deliver for him, and we hope to name his opponent within 48 hours.
"Our thoughts are with Kiko and his family at this time and we wish them well."
One man who will not be filling the void is Willie Casey.
The former European champion is preparing to face Daniel Kodjo Sassou in Belfast a week after but his and Frampton's camps were unable to reach an agreement and he will still be fighting Daniel Kodjo Sassou on September 17.