Annan stopped a row between Elmo and his friends
Annan guest-starred on the long-running show to help teach children how to resolve conflict.
He is only the third politician on the show in recent years - first ladies Barbara Bush and Hillary Clinton have also appeared.
Annan stepped in when puppet character Elmo and his friends argued over who would get to sing the alphabet song.
In the end he persuaded them all to join in.
Afterwards he said it was "wonderful to reach out to young people" and hoped that he showed children "the spirit of the UN, a spirit of understanding, sharing and working together".
He said some politicians needed to be more like the characters in the show: "Elmo and his friends will tell us, it's the way they are, they tell it straight.
"Keep it simple and it brings you back to earth. I think that is very important, we all need that."
The show's executive producer, Michael Loman, said Annan was a perfect guest.
"One of the things that is truly unique about Sesame Street is that we teach children about inclusiveness. Who better to illustrate that point than the secretary-general of the United Nations?" said Loman.
Annan flew to Norway after the programme where he will receive the 100th Nobel Peace Prize on Monday.
Sesame Street started in November 1969 and is now into its 29th season in the US.
The programme's original idea was to help teach children numbers and words using cartoons and puppets and it still adheres to those ideals.
Jim Henson, the man behind The Muppets, showed a world where Cookie Monsters and Big Bird lived with children and adults.
No date has been set for when Annan's appearance will be aired, but it will be part of the new season that starts on 4 February.