Elfman was born Jennifer Mary Butala in Los Angeles, California, the daughter of Sue (née Grace), a homemaker, and Richard Wayne Butala, a Hughes Aircraft executive.Elfman attended the Los Angeles County High School for the Arts as a dance major and graduated in 1989. Her uncle is Tony Butala of The Lettermen. She studied with acting teacher Milton Katselas and Richard Lawson at the Beverly Hills Playhouse before beginning her television career.
Elfman began as a professional dancer, making an appearance in UK electronic group Depeche Mode's promotional video for their 1990 song "Halo". She also toured as a dancer with the group ZZ Top. She made a switch to acting in the early 1990s, appearing in the 1993 music video "Black Lodge" by heavy metal band Anthrax. In 1995, she appeared in the Chris Isaak music video "Somebody's Crying".