WASHINGTON — Carol Burnett, who became famous for playing a variety of characters in sketch comedy routines on her namesake television show, was named the winner of the nation’s top humor prize on Tuesday.

The Kennedy Center for the Performing Arts said Burnett will receive the Mark Twain Prize for American Humor on Oct. 20 in Washington. A gala performance featuring top names in comedy will be taped and broadcast nationally Oct. 30 on PBS.

The 80-year-old Burnett said she can’t believe she is receiving the prize from the Kennedy Center. “It’s almost impossible to be funnier than the people in Washington,” she said in a statement.

Burnett had her breakout on Broadway in “Once Upon a Mattress,” performing at night in 1959 while also appearing in the mornings on TV’s “The Garry Moore Show.” She is best known for her own long-running variety show, “The Carol Burnett Show.” It ran from 1967 to 1978, averaging 30 million viewers a week on CBS. Her guest stars included Lucille Ball, Jimmy Stewart, Ronald Reagan and Betty White.

Burnett was born in San Antonio in 1933. She soon moved to Hollywood with her mother and grandmother and was raised in a small studio apartment. She received an anonymous donation to attend college at UCLA, where she studied journalism and took an acting class. Burnett moved to New York City, where she staged musical revues and performed in nightclubs. She was spotted by talent bookers and soon performed her rendition of “I Made a Fool of Myself Over John Foster Dulles” on television. Kennedy Center Chairman David Rubenstein called Burnett a “unique and beloved entertainer.”

“From her television program and appearances, as well as her performances on Broadway and in film, Carol Burnett has entertained generations of fans with her vibrant wit and hilarious characters,” he said in announcing the prize.

The Mark Twain Prize honors people who have an impact on society in the tradition of Samuel Clemens, better known as Twain, as a social commentator and satirist. Previous honorees include Bill Cosby, Steve Martin, Tina Fey and Ellen DeGeneres, who won last year.