Host Michael Kay said Thomas acted at the request of Knicks and Madison Square Garden officials, who Kay said asked that Thomas not go through with the interview after they learned of it.
Garden spokesman Barry Watkins said, "Isiah doesn't work for us." He declined to comment further.
The station had been promoting the interview with Thomas all afternoon, and it was to last about two hours and include the Florida International coach taking calls from listeners.
Kay left the air without explanation shortly after 4 and returned nearly an hour later, saying he had been involved in "intense" discussions with Thomas and 1050 executives.
At 5:45, Kay said Thomas would not be appearing, even though he still was on the floor on which the station's studios are located near the Garden.
"It became clear to Isiah that the New York Knicks did not want him to go on," Kay said.
"I don't believe that the Knicks see any good in Isiah coming on and Isiah Thomas has decided to honor that feeling by the Knicks and not come on."
Kay later said Thomas seemed torn during their meeting, and Kay said he warned Thomas he would bear the brunt of the public relations fallout if he canceled.
"I guess the Garden looks at it as an atmosphere that is much too toxic at this point and I guess their thinking is, what good comes out of it?" he said. "I would respectfully disagree with the Garden. I think a lot of good could come out of it."