Ann Dowd was born on January 30, 1956, in Holyoke, Massachusetts, the daughter of John (1926–1974) and Dolores (née Clark) Dowd. She is one of seven children (siblings, Kathleen, John, Elizabeth, Clare, Deborah, and Gregory), who were raised by their mother after her father died when Ann was a senior in high school. Her mother later married Philip Dean (1929–2010), a doctor. Her brother Gregory is a doctor of veterinary medicine and another brother, John Dowd Jr., is president of The Dowd Agencies, an insurance company started by their great-grandfather. Her paternal grandfather was James "Kip" Dowd, a former Major League baseball player for the Pittsburgh Pirates.
Dowd's family is Irish Catholic. She attended the Williston Northampton School, where she performed in school plays. Dowd became interested in acting at a young age but was dissuaded by her family at first because they did not approve of her pursuing an acting career. She graduated in 1978 from College of the Holy Cross in Worcester, Massachusetts where much of Dowd's family also attended and she was a premed student and took acting classes. Dowd credits her instructors and roommate at that time for persuading her to forgo medical school and follow her passion for acting. She traveled to New York City to audition for the Goodman School of Drama at Depaul University in Chicago, where she received an MFA in Acting. While at Depaul, Dowd received a prestigious scholarship from the Sarah Siddons Society, an award that had also gone to Carrie Snodgress. Dowd was classmates with Elizabeth Perkins and also worked as a waitress during this time.
Dowd spent several years performing in regional theatre in the Chicago area, performing often at the Court Theatre, later deciding in 1988 to move to New York City to pursue a bigger stage. She pounded the pavement and her first acting gig there was with the Hartford Stage Company.