Gwynne was born on July 10, 1926, in New York City, the son of Frederick Walker Gwynne, a partner in the securities firm Gwynne Brothers, and his wife, Dorothy Ficken Gwynne. His paternal grandfather, Walker Gwynne, was an Anglican priest, born in Camus, near Strabane, County Tyrone, Northern Ireland around 1846, who married an American woman, Helen Lea Bowers, and his maternal grandfather, Henry Edwards Ficken, was an emigrant from London, England who married an American woman, Josephine or Josephina Preston Hubbard. He had at least two siblings, Dorothy Gwynne and Bowers Gynne, who both died young. Although Gwynne grew up in Tuxedo Park, New York, he spent most of his childhood in South Carolina, Florida, and Colorado because his father traveled extensively. Fred Gwynne attended the Groton School.