Sanchez, who was born in Cuba and had worked at CNN since 2004, was host of the two-hour "Rick's List" on CNN's afternoon lineup. He did a prime-time version of that show in recent months, but that ended this week because the time slot is being filled by a new show featuring former New York Gov. Eliot Spitzer and columnist Kathleen Parker.
Stewart had frequently poked fun of Sanchez on Comedy Central's "The Daily Show," most recently for saying on the air that his show had received a tweet from House Republican leader John Boehner. Stewart called it a case of "send a twit a tweet."
"He's upset that someone of my ilk is almost at his level," Sanchez said during a satellite radio interview with Pete Dominick.
RELATED: Audio of Sanchez on radio show
Details of the interview were posted on the Mediaite website Friday and quickly became a topic of conversation in the media world.
Sanchez said that Stewart is bigoted toward "everybody else that's not like him." He said Stewart "can't relate to what I grew up with," saying his family had been poor and he had seen prejudice directed at his father.
Sanchez dismisses it when Dominick points out that Stewart, who is Jewish, is also a minority.
"I'm telling you that everyone who runs CNN is a lot like Stewart, and a lot of people who run all the other networks are a lot like Stewart, and to imply that somehow they, the people in this country who are Jewish, are an oppressed minority?" Sanchez said, adding a sarcastic "yeah."
"I can't see someone not getting a job these days because they're Jewish," he said.
CNN issued a statement late Friday that said Sanchez "is no longer with the company." In it, the network also thanked Sanchez "for his years of service" and wished him well.
Sanchez did not immediately return an e-mail or call to his mobile phone seeking comment, though it was unclear whether the CNN-issued phone or e-mail address were still active.
Stewart had no comment on Sanchez's statements, a Comedy Central spokesman said.
Three times in the past few months Stewart had used a Sanchez clip for the mocking "moment of Zen" feature on "The Daily Show," including once where Sanchez mispronounced the world "annals" in a story about Vice President Joe Biden.
He also made fun of Sanchez questioning a reporter who was stationed in a California gay bar for a report on the court case there involving gay marriage and hadn't found anyone at the bar who opposed the idea.
Sanchez spent much of his career as a reporter and anchor in Miami, where he won an Emmy Award in 1983 for a story on why he left Cuba. He has also worked at MSNBC and CNBC.
During the interview with Dominick, Sanchez told about a CNN executive whom he would not name telling him that he saw Sanchez not as an anchor but a reporter like ABC's John Quinones. He implied that this was a subtle form of bias.
Later in the interview Sanchez, indicated that "bigot" may be too strong a word to describe Stewart, saying he was "prejudicial" instead.
"He's not just a comedian. ... He can make and break careers," Sanchez said.