US-based Sesame Workshop said 52-year-old Kevin Clash denies the charges, which were first made in June by the alleged partner, who by then was 23.
"We took the allegation very seriously and took immediate action," Sesame Workshop said. "We met with the accuser twice and had repeated communications with him. We met with Kevin, who denied the accusation."
The organisation said its investigation found the allegation of underage conduct to be unsubstantiated. But it said Mr Clash exercised "poor judgment" and was disciplined for violating company policy regarding internet usage. It offered no details.
"I had a relationship with (the accuser)," Mr Clash told the TMZ website. "It was between two consenting adults, and I am deeply saddened that he is trying to make it into something it was not."
At his request, Mr Clash has been granted a leave of absence in order to "protect his reputation", Sesame Workshop said.
" 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.
Sesame Street is currently in production, but other puppeteers are prepared to fill in for Mr Clash during his absence, according to a show source. "Elmo will still be a part of the shows being produced," they said.
Mr Clash has been a Sesame Street puppeteer since 1984, when he was handed the fuzzy red puppet named Elmo and asked to come up with a voice for him. He transformed the character, which had been a marginal member of the Muppets troupe for a number of years, into a major star rivalling Big Bird as the face of the show.
In 2006, Mr Clash published an autobiography, "My Life as a Furry Red Monster," and was the subject of the 2011 documentary "Being Elmo: A Puppeteer's Journey".