She died in Los Angeles on Saturday, her family said in a statement to The Associated Press. No cause was given.
"To her family and friends, Shelley was a source of love, strength, laughter, and comfort," her family wrote.
"She had a remarkable ability to make people feel welcomed, valued, and cared for."
Fabares was born in Santa Monica, California, in 1944, and started acting as a young child.
Her first television credit came at 10 when she appeared on The Loretta Young Show.
Many movies and television shows followed: She acted with Paul Newman, Frank Sinatra and Eva Marie Saint in a Producers Showcase production of Our Town; was in the Rosalind Russell movie The Girl Rush and the Rock Hudson drama Never Say Goodbye.
Other early credits include Annette, Captain Midnight and the Black Leather Jackets episode of The Twilight Zone.
Her biggest break came when she was cast as Mary Stone on The Donna Reed Show, where she was a regular from 1958 through 1963.
During that time she also got a recording contract and had two Top 40 hits including Johnny Angel.
In the early 1960s, she also co-starred in three movies with Elvis Presley: Girl Happy, Spinout and Clambake.
"I think the years on The Donna Reed Show, the years from 14 to 19, were so incredibly important," Fabares told the Los Angeles Times in 1993.
"Donna Reed was simply an extraordinary woman, a woman of great strength, kindness, integrity and compassion. I am not trying to make her sound like a saint, but she had the most profound influence on me. I carry her with me today."
In the late 1970s, Fabares made an impression as Francine Webster on the CBS sitcom One Day at a Time.
"She also played James Caan's wife in Brian's Song. One of her biggest roles came when she was cast as Christine Armstrong in Coach, although the show took a minute to find its audience.
"I did always feel from the very beginning if they could find the right spot for us, this was a show that would last," she said in the 1993 Los Angeles Times interview.
Fabares married twice, first to producer Lou Adler in 1964. She had been married to M-A-S-H actor Mike Farrell since 1984. She was also a devoted advocate for Alzheimer's awareness, which affected her mother.
In early 1999, a visit to the emergency room for an oesophageal bleed revealed that she had progressive liver failure. After spending 22 months on a waiting list, she had liver transplant surgery in October 2000.
In an interview with Cedars-Sinai Medical Center in Los Angeles three years after the transplant, she said she'd been "changed by the experience" and was eternally grateful to Farrell who was with her "every step of the way".
Her family, in their statement, said "we will remember Shelley for her kindness, loyalty, wit, courage, and beautiful spirit. We will miss her deeply - not only as a celebrated performer, but as the loving and extraordinary person she was in our everyday lives."
