Clash, 52, had been the show's Elmo puppeteer and voice for 28 years, according to CNN.
The underage sex allegations were made public Nov 12., but then later recanted by a 24-year-old man who has chosen to remain anonymous, The New York Times reported.
Sesame Street had made plans for Clash to return to work.
But this week, TMZ claimed a second man had accused Clash of initiating a relationship 20 years ago, when the man was 15, and has now sued him for $5 million.
"Unfortunately, the controversy surrounding Kevin's personal life has become a distraction that none of us wants, and he has concluded that he can no longer be effective in his job and has resigned from Sesame Street," Sesame Workshop said in a statement. "This is a sad day for Sesame Street."
According to USA Today, production of the preschool series will continue, and Elmo will be played by understudies trained by Clash.