Salter was born in Grand Rapids, Michigan and was raised in Detroit, Michigan and Baltimore, Maryland. She received her B.A. from Harvard University in 1976 and her M.A. from Cambridge University in 1978. In 1976, she participated in the Glascock Prize contest.
While at Harvard, she studied with the noted poet, Elizabeth Bishop. She has been an editor at the Atlantic Monthly and at The New Republic.
From 1984 to 2007, she taught at Mount Holyoke College and was, from 1995 to 2007, a vice president of the Poetry Society of America.
Salter is married to Brad Leithauser, a writer, who also teaches at Johns Hopkins University. They have two daughters, Emily and Hilary Leithauser.