COOKIE MONSTER has an important lesson for Don Draper.

If you’re wondering what a fuzzy blue Muppet, adored by millions of children, could possibly have to do with the debonair protagonist of television’s “Mad Men,” you’ll have to visit the Museum of the Moving Image in Astoria, Queens. Its new exhibition “Jim Henson’s Fantastic World” shows that Henson, the designer, puppeteer and filmmaker probably best known for “Sesame Street” and “The Muppet Show,” was once quite a Mad Man himself.

Cookie Monster evolved from the Wheel Stealer, one of several puppet creatures Henson invented who consume a family’s snacks in a 1960s television commercial. He later appeared on TV chomping an I.B.M. computer. According to the exhibition, Henson had hit on something that the era’s advertising mavens had hardly considered: Humor sells products.

“He was also making fun of Madison Avenue and the way things were sold, and yet he was very successful at it,” Karen Falk, the show’s curator, said in an interview. “He was much loved by the Madison Avenue executives. Maybe having it come from a puppet character made it O.K.”

Henson the subversive advertising genius is just one of the lesser-known identities the exhibition reveals. It also portrays Henson the graphic designer, Henson the product of the ’60s counterculture, Henson the experimental filmmaker and Henson the creative collaborator. The 3,500-square-foot show, consisting of more than 120 artifacts, has come to New York as its last stop on a four-year tour organized by the Smithsonian Institution Traveling Exhibition Service. Tracing Henson’s development from his Mississippi childhood and Maryland high school and college years until his death from a bacterial infection in New York in 1990 (he was only 53), it comprises — along with a wealth of film and video — sketches, notes, photographs, television pitches, storyboards, and even doodles and office memos.