Sesame Workshop said puppeteer Kevin Clash denies the charges, which were first made in June by his alleged partner, who by then was aged 23.
"We took the allegation very seriously and took immediate action," Sesame Workshop said in a statement. "We met with the accuser twice. We met with Kevin, who denied the accusation."
The organisation described the relationship as personal and "unrelated to the workplace". Its investigation found the allegation of underage conduct to be unsubstantiated.
But it said Mr Clash – a 52-year-old divorced father of a grown daughter – exercised "poor judgment" and was disciplined for violating company policy regarding internet usage. It offered no details.
"I am a gay man. I have never been ashamed of this or tried to hide it," Clash said.
"I had a relationship with (the accuser)," Mr Clash told TMZ. "It was between two consenting adults and I am deeply saddened that he is trying to make it into something it was not."
Sex with a person under 17 is a felony in New York if the perpetrator is at least 21. It was unclear where the relationship took place, and there is no record of any criminal charge against Mr Clash in the state.
At his request, Mr Clash has been granted a leave of absence in order to "protect his reputation", Sesame Workshop said.
No further explanation was provided, nor was the duration of his leave specified.
" 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, as it has for 40 years," Sesame Workshop said in its statement.
Mr Clash has become a star in his own right and has been a puppeteer for 'Sesame Street' since 1984.
It was then that he was handed the fuzzy red puppet with ping-pong-ball eyes and asked to come up with a voice for him.
Clash transformed the character, which had been a marginal member of the Muppets gang for a number of years, into a major star rivaling Big Bird as the face of the ever-popular 'Sesame Street'.