Shannon was born in Shaker Heights, Ohio, on September 16, 1964, to an Irish American Catholic family. Her mother, Mary Margaret "Peg" (née Keating), was a teacher, and her father, James Francis Shannon, was a sales manager. Her maternal grandparents were born in Ireland, with her grandfather being from Cloghmore, Achill, Mayo. At age four, Shannon was involved in a car accident which killed her mother, younger sister, and cousin. Shannon attended St. Dominic School in Shaker Heights for grade school, and Hawken School in Gates Mills, Ohio. She attended New York University, where she studied drama and graduated from NYU's Tisch School of the Arts in 1987.