Sesame Workshop, which produces the show, said the controversy swirling around the 52-year-old Clash had become a "distraction" that could not be overcome, calling it "a sad day for Sesame Street."
Last week, Clash -- who is openly gay -- took a leave of absence from the show after a man said the pair had had sex several years ago, when the accuser was only 16 -- a claim Clash firmly denied. The man later dropped the claim.
But on Tuesday, celebrity website TMZ.com reported that a second man, identified as Cecil Singleton, had filed a lawsuit claiming the pair had a relationship when he was under the age of consent.
"Unfortunately, the controversy surrounding Kevin's personal life has become a distraction that none of us wants," Sesame Workshop said, adding that Clash "has concluded that he can no longer be effective in his job and has resigned."
"Sesame Workshop's mission is to harness the educational power of media to help all children the world over reach their highest potential," it said.
"Kevin Clash has helped us achieve that mission for 28 years, and none of us, especially Kevin, want anything to divert our attention from our focus on serving as a leading educational organization."
In a separate statement, Clash said: "I am resigning from Sesame Workshop with a very heavy heart."
"Personal matters have diverted attention away from the important work Sesame Street is doing and I cannot allow it to go on any longer," he added in the statement sent by his publicist Risa Heller.
"I am deeply sorry to be leaving and am looking forward to resolving these personal matters privately."
Last week, Clash admitted he had had a relationship with the first accuser, but insisted it occurred after the man had turned 17. Later, the accuser's lawyers issued a statement saying it was an "adult consensual relationship."
Clash was the subject of last year's "Being Elmo: A Puppeteer's Journey," a documentary narrated by Whoopi Goldberg, which won a special jury prize at the Sundance Film Festival. He has won multiple Emmy awards.
"Sesame Street," which first appeared on public television in November 1969, teaches children the basics of reading, writing and counting.
Sesame Workshop said last week that the controversy surrounding Clash would not have an impact on the show, or its furry red star.
"Elmo is bigger than any one person and will continue to be an integral part of Sesame Street to engage, educate and inspire children around the world," it said.
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