Minnie was raised in Barbados. Though she made her acting debut in 1992 release film The Zebra Man with a petty role, her foremost major role came in the film Circle of Friends in 1995. After this film, she was regular in acting circuit during the 1990s. She appeared in films like GoldenEye, Sleepers and Grosse Pointe Blank but her most successful film was the Oscar-winning film Good Will Hunting in 1997. After starting her career in the early 90s, she has acted in over 40 films till date.
In addition to films, she has been a highly successful television actress. She has been a consistent figure in small screen and has appeared in a number of series. Among those the one which made her popularity grow was The Riches. The other popular series of which she has been a part of are The Deep, About a Boy and Speechless.
Minnie’s name has been associated with several of her co-stars like John Cusack and Matt Damon. She was engaged to Josh Brolin but the couple called off their engagement. Driver dated Timothy J. Lea for a short period and together they have a son named Henry.
Minnie is a pure Vegetarian. Minnie also worked as a Guitarist and Jazz singer in London.