A lawsuit filed Tuesday in New York by 24-year-old college student Cecil Singleton accuses Clash of engaging in sexual behavior with him over a two-week period while he was underage. Singleton said they met on a gay chat line.
At a news conference, Singleton said he had no idea at the time what Clash did for a living.
In its statement, Sesame Workshop said "the controversy surrounding Kevin's personal life has become a distraction that none of us want," leading Clash to conclude "that he can no longer be effective in his job."
"This is a sad day for Sesame Street," the company said.
In a statement of his own, Clash said "personal matters have diverted attention away from the important work Sesame Street is doing and I cannot allow it to go on any longer. I am deeply sorry to be leaving and am looking forward to resolving these personal matters privately."
Singleton's lawyer, Jeff Herman, said he had been contacted by two other potential victims and expected additional legal action. The lawsuit seeks damages in excess of $5 million.
The New York-based Sesame Workshop, which produces "Sesame Street," had no comment on the lawsuit. Clash did not address the new allegation. He said previously that he had an adult and consensual relationship with the first accuser.
Clash, who had been on "Sesame Street" for 28 years, created the high-pitched voice and child-like persona for Elmo, a furry, red Muppet that became one of the most popular characters on the show and one of the company's most lucrative properties.
Clash's exit followed a tumultuous week that began on Nov. 12 with a statement from the company that Clash had requested a leave of absence following the charge by a man in his early 20s that he had had a relationship with Clash when he was 16.
Clash denied the charge from that man, who has not been publicly identified, calling it "false and defamatory."
Clash, the 52-year-old divorced father of a grown daughter, acknowledged that he is gay in that statement.
Sesame Workshop, which said it was first contacted in June by that accuser, said it had launched an investigation that included meeting with the accuser twice. Its investigation found the charge of underage conduct to be unsubstantiated.
The next day Clash's accuser recanted his charge, describing his sexual relationship with Clash as adult and consensual. Clash responded that he was "relieved that this painful allegation has been put to rest."
It was in the mid-1980s that Clash, a young puppeteer at "Sesame Street," was assigned a little-used puppet now known as Elmo and turned him into a star.
Besides his heavy presence on "Sesame Street," Elmo has been a major moneymaker for Sesame Workshop. Elmo toys probably account for one-half to two-thirds of the $75 million in annual sales the Sesame Street toy line generates for toy maker Hasbro, which took over the Sesame Street license in 2010, estimates BMO Capital Markets analyst Gerrick Johnson.
Meanwhile, Clash became somewhat of a star himself. In 2006, he published an autobiography, "My Life as a Furry Red Monster," and was the subject of the 2011 documentary "Being Elmo: A Puppeteer's Journey."
In addition to his marquee role as Elmo, Clash served as the show's senior Muppet coordinator and Muppet captain. He won 23 daytime Emmy awards and one prime-time Emmy.
Though it remained unclear who might take over performing as Elmo, other "Sesame Street" puppeteers have been trained to serve as his stand-in, Sesame Workshop said.
"Elmo is bigger than any one person," the company said last week.
Associated Press Business Writer Mae Anderson contributed to this report.