Maura McGiveney was born Mary Alish McGiveney on February 28, 1939 in Stockport, England, the daughter of "quick change" actor Owen McGiveney and Elizabeth Hughes. She studied at the Royal Academy of Dramatic Arts, and first came to Hollywood to work in film, appearing in an uncredited role as an attendant in Alfred Hitchcock's North by Northwest (1959). Primarily working in television, she was in several episodes of Perry Mason and Hawaii 5-0, and also appeared in Dr. Kildare, McHale's Navy, The Virginian, Laredo and My Three Sons.

McGiveney earned a Golden Globe nomination from the Hollywood Foreign Press Association as Most Promising Newcomer of 1966 for her role as Claire Hackett in the farcical comedy Do Not Disturb, with Doris Day and Rod Taylor. On stage, she appeared in Harvey, The Second City, and The Fantasticks, among other productions.

Maura was a comedian and singer as well as an actress. In what she hoped to be her ticket to fame, she appeared in Turn-On, a projected series similar to the successful TV show Rowan & Martin's Laugh-In. Turn-On's sole episode aired February 5, 1969, with the curvaceous McGiveney as "The Body Politic," a member of the repertory company. The rather sexually explicit themes, jokes and remarks led to ABC affiliates refusing to broadcast the second episode, and the sponsor Bristol-Myers immediately cancelled it, even though five shows were filmed and twenty-one more were planned. Maura said, "I still can't understand it. We were all so sure it was going to be a big hit."

On January 10, 1972, she married longtime on-and-off boyfriend William Szathmary, also known on television as Bill Dana, in Las Vegas, NV. The couple were divorced four months later in Los Angeles.

Maura McGiveney died of cirrhosis of the liver on November 10, 1990 in Sherman Oaks, CA. at the age of 51.