Peters was born Suzanne Carnahan in Spokane, Washington. She began working for MGM Studios after completing high school. Her first job was to read with potential actors in their screen tests. Before long she had impressed studio executives with her own talent, and they began casting her in films.

For the first two years she used her given name and played small, often uncredited parts in films such as Meet John Doe (1941), before adopting her stage name. Her first substantial role, in Random Harvest (1942), earned her an Academy Award for Best Supporting Actress nomination. MGM began to groom her for starring roles, casting her in several lesser productions that allowed her to learn her craft. A starring role in Song of Russia (1943) earned her critical acclaim but the film was not a commercial success.

Married to the actor Richard Quine, she was with him on a hunting vacation in early 1945, when a rifle accidentally discharged, causing a bullet to be lodged in her spine. The accident left her permanently paralysed from the waist down and confined to a wheel chair, however she attempted to continue her acting career. An unsympathetic role in The Sign of the Ram (1948) failed to win an audience, and a starring role as a detective in the television series Miss Susan (1951) was also unsuccessful. She toured in stage productions of The Glass Menagerie and The Barretts of Wimpole Street, and her performances were highly regarded, but her disability made her a difficult actress to cast.

Her career faltered, and as her marriage ended, Peters suffered from depression. Her health continued to deteriorate until her death, in Visalia, California, from kidney disease and pneumonia, complicated by anorexia nervosa.