Moore won the 1998 O. Henry Award for her short story "People Like That Are the Only People Here," published in The New Yorker on January 27, 1997. In 1999, Moore was named as the winner of the The Irish Times International Fiction Prize for Birds of America. In 2004, she was selected as winner of the Rea Award for the Short Story, for outstanding achievement in that genre.
She was elected to the American Academy of Arts and Letters in 2006, and is a fellow of the Wisconsin Academy of Sciences, Arts & Letters. In 2008, she delivered Oxford University's annual Esmond Harmsworth Lecture in American Arts and Letters at the university's Rothermere American Institute. Her 2009 novel, A Gate at the Stairs, was a finalist for the 2010 PEN/Faulkner Award for Fiction and for the Orange Prize for Fiction. Bark was shortlisted for the 2014 Frank O'Connor International Short Story Award and was a finalist for The Story Prize.