Krige was born in Upington, South Africa, the daughter of Pat, a psychologist, and Louis Krige, a physician. She left for London, England, in 1976. Initially she had plans to become a clinical psychologist but turned to acting after an experience in an acting class at Rhodes University. She then attended the Central School of Speech and Drama in London.

Krige made her professional debut on British television in 1979 and appeared in the television movie A Tale of Two Cities. She went on to play Sybil Gordon in Chariots of Fire and Eva Galli/Alma Mobley in Ghost Story (both 1981).

She played Bathsheba in King David (1985) and Mary Shelley in Haunted Summer (1988). She appeared on stage in plays such as Thomas Otway's Venice Preserv'd. She appeared in what she called "tons of TV" in both the U.S. and the UK. This includes made for television movies from Baja Oklahoma (1988) and Ladykiller (1992), to mini-series such as Ellis Island (1984) and The Scarlet and the Black (1993).

In Star Trek: First Contact, she played the Borg Queen, who attempts to assimilate Earth into the Borg collective. She would return to this role in the Star Trek game Star Trek: Armada II, and in the Star Trek: Voyager series finale, "Endgame" in 2001 (Susanna Thompson would play her in 4 episodes of Voyager between 1999-2000).

She was awarded the Laurence Olivier Theatre Award in 1982 (1981 season) for Most Promising Newcomer in the production of Arms and the Man. She was nominated for Best Supporting Actress at the 1992 Saturn Awards for her role in Sleepwalkers. In April 2004 she was awarded an honorary Litt.D. degree from Rhodes University.