Moss was born in Vancouver, British Columbia. In the late 1980s she moved to Spain to pursue a career in modelling. Her first television appearance was in the drama series Dark Justice. She moved to Los Angeles, California with the series with 1992. Her big breakthrough when chosen to play the leather-clad hacker Trinity in the 1999 box office success The Matrix. She reprised the role of Trinity in two sequels as well as providing voice-overs for video game and animated spin-offs of the film. She also appeared as Natalie in the critically-acclaimed Memento in 2000.
Moss married fellow actor Steven Roy in 1999. In 2003 she announced they were expecting a baby together in the northern autumn of that year.