As a child, Henson appeared in some of the filmed segments that his father produced for the PBS children's series Sesame Street.

[3] During his summer break from high school at the age of 17, Henson assisted in the production of The Great Muppet Caper (1981); skilled in the use of marionette puppets, he helped create and operate a special rigging device that allowed the Muppets to appear to ride bicycles.

He also performed the voice of Hoggle, one of the main characters in his father's film Labyrinth (1986), and the dog in both versions of The Storyteller (1988 and 1990).

Henson was the executive producer for several television series: Dinosaurs (1991–94), Aliens in the Family (1996), Bear in the Big Blue House (1997–2006) and Farscape (1999–2003).

Henson married Ellis Flyte, costume designer for the 1986 fantasy adventure film Labyrinth, in November 1990.