Amick was born in Reno, Nevada, the daughter of Judy, a medical office manager, and Bill Amick, a musician. Amick's parents are German; the name Mädchen (pronounced [ˈmɛːtçən] ), which means "girl" or "maiden" in German, was chosen by her parents because they wanted an unusual name. As a young girl, Amick was encouraged by her parents to follow her creative instincts. She learned to play the piano, bass, violin and guitar and took lessons in tap, ballet, jazz and modern dance. In 1987, at the age of 16, she moved to Los Angeles to pursue a career in acting.

She is best known for playing Shelly Johnson on the cult television series Twin Peaks and its 1992 prequel film Twin Peaks: Fire Walk with Me.

Amick has been married to songwriter David Alexis since 1992. The couple have two children.