Henson was born in Westchester County, New York, the daughter of puppeteers Jane (née Nebel; 1934–2013) and Jim Henson (1936–1990). She has four siblings: Cheryl (born 1961), Brian (born 1963), John (1965–2014), and Heather Henson (born 1970).
Henson is the CEO of The Jim Henson Company.
Besides her direct television and movie work, she has been president of production for Columbia Pictures, and an executive for Warner Brothers. She holds a degree from Harvard University, where she majored in folklore and mythology and served as president of the Harvard Lampoon. She has also served on the Board of Overseers.