Feldon was born Barbara Anne Hall in Bethel Park, Pennsylvania, and grew up in Pittsburgh. She graduated from Bethel Park High School and trained at Pittsburgh Playhouse. In 1955, she graduated from Carnegie Institute of Technology (now Carnegie Mellon University) as a bachelor of arts in drama. She was initiated into the Delta Xi Chapter of Kappa Kappa Gamma. In 1957, she won the grand prize on The $64,000 Question in the category of William Shakespeare.