Kevin Clash denies the charges, which were first made in June. The alleged partner is now in his mid-20s.
Sesame Workshop said its investigation found the allegation of underage conduct to be unsubstantiated, but it said Clash exercised "poor judgment."
"We took the allegation very seriously and took immediate action," Sesame Workshop said in a statement issued Monday. "We met with the accuser twice and had repeated communications with him. We met with Kevin, who denied the accusation."
Sesame disciplined Clash, 52, for violating the company's Internet policy, but offered no other details.
"Kevin insists that the allegation of underage conduct is false and defamatory and he is taking actions to protect his reputation," Sesame Workshop said in its statement.
"Sesame Street" is currently in production, but other puppeteers are prepared to fill in for Clash during his absence, according to a person close to the show.
"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.
Clash, the divorced father of a grown daughter, has been a puppeteer for "Sesame Street" since 1984.
The Associated Press contributed to this report.