McGovern started acting in plays in high school. Agent Joan Scott saw her performance in The Skin of Our Teeth by Thornton Wilder, was impressed by her talent, and recommended that she take acting lessons. McGovern followed her advice and studied, first at the American Conservatory Theater in San Francisco, and then at The Juilliard School in New York City.

While studying at this school, she was offered in 1980 a part in her first movie, Ordinary People, in which she played the girlfriend of troubled teenager Timothy Hutton. It was also Robert Redford's first film as director. The movie won four Oscars. The next year she earned an Academy Award nomination as Best Supporting Actress for her portrayal of the 19th-century actress Evelyn Nesbit in the movie Ragtime. The following years she completed her education as an actress at the American Conservatory Theatre and at The Juilliard School, and began to act in theater plays, first off-Broadway and later in famous theaters. Since then she has continued performing on stage between film assignments rather than concentrating on becoming a film star. As a movie actress, big-eyed and slightly baby-faced McGovern has given preference to eccentric roles over those parts typically tailored for actresses of her age. Besides cinema and theater, she has also played in several television films.

In 1992 she married English producer and director Simon Curtis, with whom she currently lives in London, together with their two daughters.