In its statement Tuesday, 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."
As the announcement was made, a lawsuit was being filed in federal court in New York charging Clash with sexual abuse of a second youth. The lawsuit alleges that Cecil Singleton, then 15 and now an adult, was persuaded by Clash to meet for sexual encounters.
The lawsuit seeks damages in excess of $5 million.
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. Sesame Workshop produces "Sesame Street" in New York.
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 by the accuser in June, said it had launched an investigation that included meeting with the accuser twice and meeting with Clash. 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."
In addition to his marquee role as Elmo, Clash had served as the show's senior Muppet coordinator and Muppet captain. He won 23 daytime Emmy awards and one prime-time Emmy.
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."
Though it remained unclear who might take over for Clash 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.