Ponsot was born in Queens, New York, where she and her brother also grew up. She was already writing poems as a child, some of which were published in the Brooklyn Daily Eagle. After graduating from St. Joseph's College for Women in Brooklyn, Ponsot earned her master's degree in seventeenth-century literature from Columbia University. After the Second World War, she journeyed to Paris, where she met and married Claude Ponsot, a painter and student of Fernand Léger. The couple lived in Paris for three years, during which time they had a daughter. Later, Ponsot and her husband relocated to the United States. The couple had six sons before divorcing.
Upon returning from France, Ponsot worked as a freelance writer of radio and television scripts. She also translated 69 children's books from the French, including The Fables of La Fontaine.
She co-authored with Rosemary Deen two books about the fundamentals of writing, Beat Not the Poor Desk and Common Sense.
Ponsot teaches a poetry thesis class and writing classes at the Poetry Center of the 92nd Street Y. She has also taught at the YMCA, Beijing United University, New York University, and Columbia University, and she served as an English professor at Queens College in New York, from which she retired in 1991.
Ponsot is the author of several collections of poetry, including The Bird Catcher (1998), a finalist for the 1999 Lenore Marshall Poetry Prize and the winner of the National Book Critics Circle Award, and Springing: New and Selected Poems (2002), which was named a "notable book of the year" by The New York Times Book Review.
Among her awards are a creative writing grant from the National Endowment for the Arts, the Delmore Schwartz Memorial Prize, The Robert Frost Poetry Award, and the Shaughnessy Medal of the Modern Language Association.