Fabares, who also appeared on sitcom Coach from 1989 to 1997, starred alongside the King in three movies: Girl Happy, Spinout and Clambake.
A family statement read: “To her family and friends, Shelley was a source of love, strength, laughter, and comfort.
“She was a devoted wife, cherished stepmother, daughter, sister, niece, aunt, family member, and loyal friend whose warmth, generosity, humor, and grace made an enduring difference in the lives of everyone who knew her.
“She had a remarkable ability to make people feel welcomed, valued, and cared for.
“For millions, Shelley was a beloved actress whose work became part of the fabric of American television and film,’ the statement continued, highlighting some of her most popular work – as well as her Billboard chart-topping number one single, Johnny Angel.
“But to those closest to her, her greatest legacy was personal: the love she gave so freely, the friendships she treasured, and the family bonds she held dear.”
No cause of death was given.
Fabares, who had a liver transplant in 2000, was born in Santa Monica, California, in 1944, and was the niece of actress and singer Nanette Fabray, who co-starred with Fred Astaire in the 1953 movie musical The Band Wagon and later played Fabares’ mother on Coach.
After making her acting debut aged three, Fabares first television appearance came in 1954 on an episode of The Loretta Young Show, with her co-stars the next year including Frank Sinatra and Paul Newman in the Producers’ Showcase adaptation of Our Town.
She also appeared on Annette in 1958, a TV serial that ran on The Mickey Mouse Club and featured one of its original stars, Annette Funicello, before becoming a fan favourite among teens on The Donna Reed Show from 1958 to 1965.
Fabares signed a recording contract and released two albums, despite joking that she couldn’t sing. Alongside her No1 single Johnny Angel, she also had top 40 hits with Johnny Loves Me and Ronnie, Call Me.
After a period of TV guest roles in the ’60s, Fabares earned a Golden Globe nomination for playing the wife of Chicago Bears athlete Brian Piccolo (James Caan) on the 1971 ABC television film Brian’s Song.
Regular roles on The Brian Keith Show and Forever Fernwood followed, before she played against type as the villainous Francine Webster on sitcom One Day at a Time.
After starring in 1983 TV film Memorial Day with Mike Farrell, the pair tied the knot; Fabares had previously been married to record and film producer Lou Adler, wedding in 1964 but separating in 1966 and later divorcing in 1980.
In 1989 she landed her role as Christine Armstrong on Coach, which brought her two Emmy nods and became a hit after it moved in the schedule to air after Roseanne.
Following Coach’s end, she voiced Martha Kent on Superman: The Animated Series, as well as for a 2003 episode of Justice League and the 2006 direct-to-video film Superman: Brainiac Attacks – which became her final role.
She is survived by her husband and stepchildren, Erin and Michael.