Swedberg was born in Honolulu, Hawaii, the daughter of Kay, a high school English Teacher, and Jim Swedberg, a laser Physicist. She was raised in New Mexico and attended Sandia High School in Albuquerque from 1980 to 1984. Since 1994, Swedberg has been married to Philip Holahan, and they have two children together.

Following graduation she moved to Kentucky, where she spent a year at the Actors Theatre of Louisville, following which she acted in her first film role, Norman Jewison's 1989 In Country. She followed that with roles in the 1990 movies Welcome Home, Roxy Carmichael and Kindergarten Cop and the 1991 movies Too Much Sun and the Jim Abrahams comedy spoof Hot Shots!

While living in Hawaii, Swedberg grew up playing the ukulele. In 1992, when playing the role of a singer/songwriter for a television pilot, she began playing the instrument again. She now sings and plays the ukulele in her band, Heidi Swedberg and The Sukey Jump Band. The band released an album entitled PLAY!, in 2009 and "My Cup of Tea" in 2013. She has another band called the Smoking Jackets which plays ukulele festivals and night clubs. The members, Daniel Ward, Craig McClelland and John Bartlit, are multi-instrumentalists who also teach at ukulele festivals.

Swedberg was not in Seinfeld's fifth season in 1994 but acted regularly in parts on other television shows, including Empty Nest, Murder, She Wrote, Star Trek: Deep Space Nine, and Grace Under Fire.