A native of Cincinnati, Ohio, Green was born in 1927. Her father was a foreign copyright and trademark agent, like his fictional counterpart in The Dead of the House, and her mother was a homemaker. She attended Wellesley College, studying with Wallace Stegner and receiving her Bachelor of Arts degree in 1948. She later went to Stanford University, receiving a Master's degree in 1956. While at Stanford, she studied with the celebrated Russian writer, Vladimir Nabokov.
In the early 1960s she began writing what would ultimately become The Dead of the House. In 1970, she was hired as a professor by Columbia University, a position that she held until her retirement. Initially The Dead of the House was published in a shorter form in The New Yorker; in 1972 it came out in novel form and attracted critical and commercial attention. In 1985 In the City of Paris, a juvenile novel about French culture and the wonders of Paris, was published.
Green died of lung cancer on October 16, 1996, in New York City. At the time of her death, she had completed Golden Spark, Little Saint: My Book of the Hours of Saint Foy, which has never been published.