Henry has been voicing Cleveland since Family Guy first premiered in 1999, and carried on the role in the character's spinoff series, The Cleveland Show, from 2009-2013.
The state of play: One character on the show, Apu, was seen as an offensive caricature that "perpetuated ugly stereotypes about South Asians" to many Indian Americans and immigrants, the New York Times' Vikas Bajaj wrote in 2018.
The announcement came as Mike Henry, the white actor who voices the black character of Cleveland Brown in Family Guy, another animated series produced by Fox, announced on Twitter that he was giving up the role.
That will affect characters such as Dr Julius Hibbert, voiced by Harry Shearer, and Homer's friend Carl, voiced by Hank Azaria.
A number of white actors have recently announced that they will step back from voicing non-white characters on animated shows.
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The decision includes a recurring character from the series, launched in 1989 - Apu Nahasapeemapetilon, a grocer of Indian origin voiced in the American version of the show by white actor Hank Azaria.
"Moving forward, The Simpsons will no longer have white actors voice non-white characters", the producers said in a short statement.
There have been no other reactions yet from the show producers or cast members.
The announcements come amidst a widespread reckoning for U.S. pop culture about racism following mass protests this month over the killings of Black Americans by police. "We all feel like it's the right thing".
That show's creator, Raphael Bob-Waksberg, wrote on Twitter about his regrets over the decision, saying he meant to "write AWAY from stereotypes and create an Asian American character who wasn't defined exclusively by her race". This week alone, Kristen Bell from Central Park and Jenny Slate from Big Mouth said, within hours of each other, that they would no longer voice Black characters.
"Casting a mixed race character [with a] white actress undermines the specificity of the mixed race and Black American experience", she added.