Finkelstein was the second child of Louis and Rasha (Rae) Shapiro, clothing merchants in Manhattan. Her brother, David I. Shapiro, became a noted Washington lawyer. As a girl, Finkelstein led what she calls “a bifurcated life, half American, half some idea of upper bourgeois European society. This upbringing maintains itself in many of her poems as mood, or attitude, or actual subject matter.
She was married at nineteen to Jack Finkelstein, a pediatric neurologist. They had three children: Adam, Gabriel, and Nicholas. She divorced in 1977 and later married the poet Robert Clinton, whom she also divorced.
Having dropped out of Barnard College after one term, she earned an M.F.A. at Goddard College, where she studied with Ellen Bryant Voigt, Robert Hass, and Michael Ryan. She was at Yaddo and MacDowell.
She has published her work in Poetry, The Gettysburg Review,]Fence, Paris Review, Seneca Review, New American Writing, and The American Poetry Review.